This question is particularly about the ancient times, up until the middle ages.
In modern history, Napoléon is well known to have been a good public speaker and to have delivered frequent speeches to his soldiers before and after battles. The integrality of his Discours de Guerre were recently reedited by the Editions Pierre de Taillac. They are not long addresses but rather proclamations and/or short motivational addresses (which would have last around 5 min, and could be easily printed in a page) but some of the most famous addresses are :
the discours des Pyramides, on the moments before the battle at the Pyramids in Giza, Egypt on Jul. 21st, 1798 ; whose famous first words ("Soldiers, think that from the top of those pyramids, 40 centuries are beholding you") are still very famous (and a recurring joke in one of the Astérix comic books, but that is another story).
the discours d'Austerlitz, which he delivered after the most famous battle of his career, on dec. 2nd, 1805, whose first words are also extremely famous ("Soldats, je suis content de vous"). The integrality of it is available (here)[https://fr.wikisource.org/wiki/Proclamation_apr%C3%A8s_la_bataille_d%E2%80%99Austerlitz]. There is also a less famous proclamation he delivered in camp before the battle, whose text can be read (here)[https://fr.wikisource.org/wiki/Proclamation_au_bivouac_avant_la_bataille_d%27Austerlitz].
Those battles are a major part of the Napoleon legend, and as a consequence their definitive texts can differ from what was effectively said on those days (may have been reedited for publication afterwards for additional propaganda efficiency), but the fact that such proclamations occured is historical fact^1.
As it is well known, Napoléon had a deep fascination (as did many of his contemporaries of the late part of the French Revolution) with Roman and Greek models (which is made obvious looking at furniture from this era). Delivering a proclamation to ones troops before battle was expected in the Roman world, to such an extent that most historians would compose, in their narration of major history battles, an address (again, usually without certainty to their accuracy, and often simply reimagining the key points that would have been exposed by the military commander to its troops : think Thucydides and Périclès's speeches in the Guerre du Péloponnèse, who systematically rewrote elegant speeches befitting of Périclès's character to underline the debates going on at the time) : the usual latin word fo this is exhortatio. You can find examples for instance in Livy ( Ab Urbe Condita, XXVII, with the *exhortatio by Hannibal at Canusium). In practice such addresses would probably have been less formal, and due to the number of troops and the absence of sound amplifications, would have been retold in substance by direct superiors of soldiers, or read as proclamations. Nonetheless, significant oratory skills were expected of a military commander (and they are a talent much emphasized by ancient historians in famous figures of successful generals such as J. Caesar) : after all, a Roman consul commanding his troops was an elected official.
^1 : (in the case of Austerlitz) Jacques Garnier (préf. Jean Tulard), Austerlitz : 2 décembre 1805, Paris, Fayard
Pre-battle speeches were an expected part of classical generalship, especially before a major battle. However, they were usually given the day before rather than just prior to the start of the battle, with a few exceptions.
The pre-battle speech was a way for generals to bolster their men's morale by reminding them what they were fighting for. Particularly memorable passages frequently made their way into chronicles and narrative histories. For example, when the Eastern Roman Empire fought an all-or-nothing battle against the Sassanian Empire in the Last Great War of Antiquity, in which they were outnumbered at least two to one, emperor Heraclius is attested to have said this to his men:
"Brothers, do not be troubled by your enemies’ numbers for, God willing, one will chase thousands. Let us sacrifice ourselves to God for the salvation of our brothers. Let us take the martyrs’ crown so the future will applaud us and God will give us our reward.” - he's basically telling them that God will reward them for fighting to the death.
However, the idea that you often see in film or in games of generals addressing their men after they are in formation and facing their enemy is mostly a fantasy. As M. H. Hansen discussed in an article called "The Battle Exhortation in Ancient Historiography: Fact of Fiction?", generals could not have addressed their men just before a major battle because the battle line often stretched over a kilometer and there is no way their voice could travel that far and be clearly audible. They also had more important things to do, like make sure the men were in the proper formation and communicate any last minute alterations to tactics and strategy now that the enemy formation was visible. Instead, the general would usually go around the camp the day before and give speeches either to the whole army assembled in the small area of the camp, or in smaller groups. The 2nd century BC historian Polybius tells us that this is what Hannibal and Aemelianus Paullus did the day before the Battle of Cannae, and what Scipio did the day before his assault on Carthago Nova. Thucydides, who was a general himself, recalls how admirals would give speeches before embarkation because it would be impossible to give a speech to everyone at sea.
Now, I said that speeches right before a battle were mostly fantasy. There were a few generals who did attempt to give speeches just before combat commenced as a regular part of their duties. It was the optimal time to give a morale-boosting exaltation, so many generals tried to fit one in. Caesar's Gallic Wars makes it clear that he was one of them:
"Caesar had to do everything simultaneously: display the flag which was the signal for running to arms; sound the command on the trumpet; recall the soldiers from their work; summon those who had gone rather further to collect material for the rampart; set his line in order; exhort the soldiers; give the command. Shortness of time and the enemies' approach prevented a great part of these."
In this case, the speed of his enemy (the Nervii) meant that Caesar did not have time to give a speech, but his account makes it plain that he fully intended to as the last thing before giving the order to attack, and that this was normal for him. However, this passage also shows one of the main reasons why this wasn't overly common - the enemy could just attack whilst the general was still speaking. For the aforementioned practical reasons, Caesar's speeches would not have been given to the whole army but in groups. He would have gallopped from one end of the line to the other, stopping at regular intervals to give the speech.
In really important battles, pre-battle speeches of the type you see in media were given, though not the whole army at once. Like Caesar, they would have 'spoken down the ranks' (Polybius), which means they started at one end of the battle line and repeated a speech at regular intervals, then gave the order to attack once at they other end. Polybius informs us that this is what Hannibal and Scipio Africanus did before their climactic showdown at the Battle of Zama and it is what Heraclius did just before his battle against three Persian armies.
So to answer your question, we do have written records of pre-battle speeches. However, most of these would have been given the day before rather than just before attacking because it was more practical. Because movies focus overwhelmingly on great battles, many depictions will be authentic, but historically the Hollywood pre-battle speech was only given before vitally important battles if generals like Caesar could find the time to fit them in.