The British decision to create a Jewish state in Mandatory Palestine was the result of, by the point of the Balfour Declaration which officialized the British support of such a plan, many decades of Jewish population growth in the region through the blooming of local communities and the arrival of Jews from abroad to join their brethren in their historic homeland.

It should be made clear from the start that the Balfour Declaration was a relatively late entry to the game. Jews had been in the region for as long as anyone had written in an alphabet, and the Roman expulsion following the Romano-Jewish wars is not believed to have ended the presence of a Jewish majority in the region. It would be a few centuries longer until the Israelite population of Jews and Samaritans would be brought to a minority, and replaced with an Aramaic-speaking Greco-Syrian Christian majority.

This was not the end of the Jewish presence, simply the start of it being a minority. The population would rise at several points, only to be brought down again by violent means such as foreign invasions or pogroms. As early as the Middle Ages, the first plans for the diaspora to resettle in the homeland came about, and by the Early Modern era the refugees of the Spanish Inquisition brought a new wave of life to the idea.

So, this is the backdrop to the beginnings of the modern Zionist movement. From the Jewish perspective, their people are forcibly scattered, driven from their homeland, and brought under heel when they recover. The migrations start to pick up speed, though, and the Jewish population is growing bit by bit. Some places, though rare, get an unstable Jewish majority. Things really kick in around the 19th century, though. That's when modern Zionism as we consider it was born.

In 1808, the city was about a quarter Jewish, a quarter Christian, and half Muslim. 2000 Jews, 4000 Muslims, and 2000 Christians, at least roughly. A decade later, dispute comes about whether there are actually more Jews or Muslims in the city. This really picks up in the 1840s, where only half-reliable data reported by various foreign officials trying to take some crude census. One Prussian says there are more Jews, another says there are more Muslims but only if you count only the men, while an Ottoman census says there are more Muslim citizens but says nothing for the total population. By 1864, the British embassy reports there are now twice as many Jews as Muslims, and that Jews are an absolute majority of the population. These fluxes could be potentially attributed to different means to count population (families, males-only, individuals, etc.) or due to Jewish and Muslim immigration and emigration. Point is, data's hard to stand by solidly for a long period of time, but the area was in contention a full century before the foundation of the State of Israel.

In the 1880s, the First Aliyah began, with Jews from Eastern Europe and Yemen migrating en masse almost like a form of permanent pilgrimage to their ancestral homeland. The Second Aliyah began in the 1900s, leading up to World War 1. Although relatively small in the grand scheme of things, I raise this to emphasize once more that these sorts of mass return-migrations were not an isolated incident, and were kept up for decades prior to the establishment of Israel. Many of these Jews were fleeing from persecution, pogroms, violence inflicted upon them, and figured that lands of opportunity such as the US and Ottoman Syria which, at the time, included the historic region of Palestine.

The Third Aliyah came after the Balfour Declaration, and so I suppose it might pertain slightly less to your question, and thus I shall not dwell on it. The reason the British chose to support the creation of a Jewish homeland in the region is, as you said because there are historical reasons behind it - Jews are not only natives of the land, who have the holiness of the land itself embedded within the culture and scripture and had a diaspora that for millennia called for a return to the land at regular intervals, but the area had been in contention between Jews and Muslims a full century before the British made their declaration.

Now, this answers your question, but I feel the need to delve on the Madagascar Plan just a bit. It does not speak well to consider it a viable alternative, if you do so, and here's why:

The Madagascar Plan was formulated by the Nazis, with the intention of creating a new ghetto far from Europe in a hostile terrain that they did not consider to be livable. The idea was, in essence, to exterminate the Jews by confining them to an island that would kill them. The island was to be run by the SS with brutality, and the plan was only canceled because the British blockade prevented the mass shipment of Jews to an island on the other side of the world. It was an important step towards the Final Solution, which would replace the Madagascar Plan and fulfill the same purpose.

Giving it the benefit of the doubt, though, there were pre-Nazi questions about settling Jews in Africa. The one I, personally, have heard of most was the Uganda Plan, but the issue with this is that it had only conditional support as a temporary refuge - to save Jews from pogroms in Europe and give them a base from which to continue on later to Palestine. Plans involving Madagascar predating the Nazi plan found that the island was not viable to house a large number of families, which the Nazis would pull on later as part of their plan. Most of all, though, the Jews didn't want that land. It had no meaning to them, they had no connection to it, but geographical Palestine was the ancient homeland revered throughout all scripture and every year's chant of "Next year in Jerusalem!"

There's also the issue that you ask why not move the Jews to Africa as if it were any better, because the same issues would arise. Both Uganda and Madagascar already had sizable permanent populations of their own. Even completely disregarding the longstanding Jewish presence and continual growth in Ottoman Syria prior to the Balfour Declaration, there is really no benefit to settling in Africa instead since the exact same problems settling in Syria/Palestine would happen anyways. They might as well go for the one Jews actually want and had been lobbying for and trying to fulfill for over a century by that point, than the one that really none of them were asking for as a permanent solution.