Easy.
The wrestling contests of the greeks were based on the greco-roman throws combined with submissions.
Wrestling contests are one of the oldest themes of pre-doric greek writing (which is written in Linear B). Linear B writings mention organized submission wrestling contests more than 1000 years before the birth of Chirst. It is mentioned in late pre-Doric literature including Homer's works.
Boxing emerged somewhat later. However, by the early doric period, boxing supplemented wrestling as both a component of military training and as a sport.
By 684 B.C. (according to wikipedia... I had to look up the date), an Olympic game called pancration was introduced. This was intended to answer the question of whether wrestling or boxing was better. The point was apparently moot already, as military men trained in both. In any case, what emerged as a winning strategy came in the form of the early powerhouse in the games, Sparta. Spartan fighters often essentially ground and pounded their opponents, throwing them to the ground, mounting them and then finishing them with strikes. When biting and eyegouging were banned, however, Sparta withdrew from pancration competitions. At this point, submissions and standup fighting began to compete effectively with the spartan strategy. Other city-states would compete to great sucess.
At the outbreak of the Pel. war, pancrationists were often placed at the head of military training programs, and pancration at this point began to displace seperate boxing and wrestling programs.
Alexander the Great considered pancration as one of the most important indicators of soldiers abilities, and pancration tournaments were used to fill empty command positions in his army. His personal bodyguards were mostly pancrationists as well.
With the coming of the roman empire, pancration became less common, as the Romans generally prefered to treat wrestling and boxing as seperate components of military training. The Roman close range fighting was based in no small part on the submission style wrestling of the greek military, and wrestling and boxing matches were very common througout Roman history.
With the fall of the roman empire, wrestling remained a major part of battlefield training for the military elite - knights and mercenaries. This may have been the origin of the pin rule - a pin in practice would have symbolized an ability to control the opponent long enough to use a secondary weapon from a dominent position.
Variations on the greco-roman submission style led to ringkampf, a german submission wrestling style that also apparently included rapid-fire punches and knifework on the ground. Most of ringkampf has been lost, but it became the main military training component for the late Teutonic knights, as well as german knights of all stripes - it later spread into italy and may have influenced Turkish and russian wrestling as well. Some parts of it remain because the training manuels were quoted in later works.
The English and Dutch also created their own unique variations - which still exist today as "Catch wrestling."
Though boxing had been in decline, it was hardly lost - as armies professionalized, boxing came back into heavier military use for less armored troops.
The advant of the firearm changed all this. Ringkampf was forgotten... greco-roman wrestling became far less common, and was ussually now done for a pin rather than a submission.
Boxing was hardly dead. In the Napoleonic wars, manuels on boxing were distributed to military commanders on all sides and it is unclear who started the idea of standardized army-wide boxing, but the manuels of the time make it clear it was expected, if not always followed up on. It was intended as a close combat system.
Boxing remains a part of standard military training in the western world to this day, although now it is ussually simply a part of the general military combatives program - a WWII era development.
I take it you already know the history of BJJ and Muay Thai, the other two major MMA styles.
I'll look forward to that.
