Really interesting question, it actually depends quite a lot on what you mean by terrorism. I say that in part because the word itself is poorly defined but also because terrorism today has almost an ideology of its own, or at least a particular MO that helps define terrorism. Contemporary terrorism is spectacular and heavily media focused. So while we might look at pre-media era massacres and say "hey, that looks like terrorism" the people who carried it out and the people who viewed the massacres might just have thought that this was a particularly brutal group.

Partly for that reason and partly because their religious ideology was so weird in comparison with later groups I'm going to skip over the Assassins and a number of incidents that I'll list at the end (which you might want to look into further) and instead jump ahead to the Al Saud.

One of the the most important early fundamentalist movements within Islam was the rise of the First Saudi State that followed the Wahhabi sect/ideology that is still predominant in Saudi Arabia (and followed by terrorist groups) today.

The austerity of their version of Islam, which decries the sanctity of shrines and Islamic saints as irreligious innovation at best and polytheism at worst drove not just their fanatical conquest of the Arabian peninsula in the late 18th/early 19th century, it also led them to engage in what might be an early precursor of terrorism when they sacked Karbala, killing thousands (whom they viewed as unbelievers, employing the doctrine of takfir) and when they attacked the annual Haj pilgrimage sent from Constantinople. The Ottomans reacted harshly, they tasked the ruler of Egypt, Muhammad Ali Pasha, to put down the Saudis, which his son and best general succeeded in doing by taking back the territory and capturing much of the House of Saud who were then executed in Istanbul.

After the wahhabis, who at least ideologically if not tactically are the intellectual ancestors of modern terrorism I would point to the foundation of the Muslim Brotherhood in Egypt in 1928 as the other pivotal pre-WWII moment in the rise of terrorism.

I think the two related points to emphasize here are that the Muslim Brotherhood was formed 1. in a mood of intense anti-colonialism as a your question suggests but 2. but also part of the broader fascist/communist/anarchist/XYZ militant political climate of the interwar period.

In other words, the Muslim Brotherhood initially formed its paramilitary apparatus not because they were Islamist terrorists but because that's what all of their political rivals were doing and in turn because that's what many European political movements were doing. Egypt, like Italy, like Germany, had huge "coloured shirt" paramilitaries for each of the major ideologies and the Muslim Brotherhood was just one of many in Egypt in the 1930s that was doing this including the Wafd, the Communists, the Socialists, etc.

Nonetheless, structurally and ideologically, if to a lesser extent tactically, the pre-WWII Brotherhood looked quite a lot like a terrorist organization. It had a militant ideology, collected weapons for use in direct action, and crucially employed a clandestine cell structure. In Brotherhood terminology this is called the Usra, or family and plays a key role in the society's organization down to this day.

That being said, it's not until after World War II that they really start to carry out what we would identify as terrorism and particularly with the wars in Palestine from 1947-48 and following the Free Officers Movement that brought Nasser to power in 1952.

It's at that time, for instance, that the Muslim Brotherhood first conceives of the use of a suicide bomb vest to assassinate Nasser, but at the time they reject the idea as being too extreme.

Despite these pre-WWII groups and ideologies, if we're talking about what we identify as the tactics of modern terrorism, that really is invented after WWII and is really most concretely developed by non-Islamist groups, particularly leftist Palestinian groups like the Abu Nidal Organization and the PFLP which most notably carried out large scale plane hijackings.

Going back to definitions again, there are also a number of groups that I think if they emerged today we would describe as Islamist terrorists, but that I think in historical context look more like insurgencies or at the very least are not really part of the genealogy of modern Islamist terrorism. These include the Mahdist uprising in Sudan, the Dervish State in Somalia, the Palestinian Black Hand organization led by Izz ad Din al Qassam, Omar Mukhtar's anti-colonialist struggle in Libya, the Faqir of Ipi, the Fakir Saidullah who led the siege of Malakand, some aspects of the 1857 Indian Mutiny and various other uprisings and rebellions by Muslims that had strong religious overtones (or explicit calls to jihad) and that resulted in civilian atrocity or asymmetrical tactics associated with terrorism but that I don't think really qualify because they're not really examples of fundamentalist Islamism.

Sources: on the Muslim Brotherhood Timothy Mitchell's The Society of Muslim Brothers. Eugene Rogan's "The Arabs: A History" for various issues relating to the rise of terrorism in Arab lands. I'm not sure I have a great single volume source to point to on the first Saudi State or on Wahhabism but there's quite a lot of writing about Wahhabism available online and in print.

edit: another group that might be interesting if much much older (i.e. 7th century AD,) if only because they are often compared with ISIS, are the Kharijites and particularly the Azraqia who declared all Muslims outside of their group to be non-Muslims and carried out banditry and massacres (what we might today view as terrorism) from their stronghold in modern south-east Iraq and north -east Arabia. W.M. Watt's "The Formative Period of Islamic Thought" has some good chapters on these groups.

I'm going to have to disagree with the other reply regarding Wahhabism as the predecessor to modern Islamic terrorism. Modern terrorism predates rise of Islamic terrorism by quite a few decades. We really only see the beginnings what we think of today as "Islamic Terrorism" in the 1970's. Al Qaeda was only formed in 1988. Prior to the 90's and 00's terrorism was more associated with anarchist, leftist, and independence movements across the world. That's why we see the FBI statistic that Islamic Extremists made up only 7% of the terrorist attacks in the US between 1980 and 2005. If the statistics had been compiled between 1970 and 2005, that would be an even lesser percentage.

We can perhaps trace Islamic terrorism back to the Palestinian cause. Certain Palestinian groups began using what we call terrorism in the late 1960's and early 1970's. But these were not Islamist organizations, they were very much leftist and socialist organizations. The founder of the PFLP was a Palestinian Christian. This was a reflection of broader political ideas in leftist and socialist organizations that saw "terrorism" or at least violence acceptable in the furthering of their cause.

A huge moment in the history of Islamic terrorism was the Soviet invasion of Afghanistan. It cannot be stressed how important this event was. The invasion brought many fundamentalist Muslims to Afghanistan to fight the Soviets. This helped them to better coordinate and organize. This was also seen to a lesser extent during the war in the Balkans and Chechnya in the 1990's. The Iranian revolution in 1979 also had a significant influence on how Muslims began to organize as well.

After the collapse of Arab Nationalism in the Middle East and then later the Soviet Union, leftist and socialist politics (especially in the Middle East) began to recede. "Religion" tended to replace these leftist and socialist ideologies, giving us what we see now. So that's why I don't think religion is actually very important in and of itself when it comes to understanding the history of Islamic terrorism. Even shaikhs in Saudi have come out in opposition to terrorism. Instead I think its better to look at the history of terrorism itself (whatever that really is) and the geo-politics from the 1950's until today, because terrorism is ultimately about politics.

So to answer your question, modern Islamic terrorism is very much a product of Cold War politics. The Soviet invasion of Afghanistan was a huge catalyst in organizing terrorist groups like Al Qaeda. Fighting off communism was a goal shared by both the US and early Islamic terrorist groups. The collapse of leftist politics starting in the 80's and exacerbated with the dissolution of the Soviet Union, meant that many turned to "religion" as the main ideology from which to organize around.