There are few remaining documents with details of the fighting art's origins.  Thailand's early historical notes, along with certain treasures, relics, works of art and documentation, were put to torch by the Burmese when the city of Ayuddhaya was overrun in 1767.
They do know that during the reign of King Naresuen the Great (1590 - 1605) that Muay Thai was part of military training.  The King himself was an expert in individual combat techniques and won several contests, which had considerable historical consequences.   In 1577, as a Prince, at the age of 22 he was declared a national hero for his Muay Thai skills.

Muay Thai reached the height of it's popularity during the reign of Pra Chao Sua "The Tiger King" in 1709.  SIAM (former name of Thailand) went through a peaceful period with it's neighbours.  Muay Thai became the favour of the population, with young and old, rich and poor joining fighting camps.   Every village staged it's own fights and heavy betting transformed ordinary bouts into vicious battles.
Peace never lasted long in Asia, and many wars continued.   With this, a number of hero's arose from the battlefields.
Amongst the greatest was "Nai Khanom Tom" who was captured and enslaved by the Burmese army along with many more countrymen.  The Burmese King realised that there were a lot of Muay Thai fighters amongst his prisoners.  He therefore organised Muay Thai fights for his entertainment.  Nai Khanom Tom was the greatest fighter and the King suggested that he fought 12 of his top warriors and if he defeated them all, he would be set free.

A ferocious  battle commenced and one by one Nai Khanom Tom defeated each warrior, until there were no more standing.  The King kept to his word and granted Nai Khanom Tom his freedom along with wealth and treasures.  This freedom day is still remembered today, Match 17th as National Muay Thai Day.
King Rama who came to the throne in 1868 loved and adored Muay Thai so much that he spent much of his life trying to popularise it.  His work was the first step in making the art the sport and art that it is today.  He personally organised Muay Thai contests where the winners were invited to participate in a supreme contest at the Royal palace in Bangkok before the King himself.  This yearly tradition is held to this very day, now known as the Kings Birthday Fights, where the best fighters from all over the world are invited to fight Thailand's best fighters.

In 1914 Muay Thai was first seen by foreign traders.   At this point it was still gruesome with very little rules.  In 1927-1930 the western influence of wearing boxing gloves was bought to Muay Thai, also weight categories, timed rounds, groin protection etc were all introduced to make Muay Thai more humane.

Muay Thai is now one of the biggest Full Contact Martial Arts in the world and also plays a huge part in MMA (Mixed Martial Arts) where the vast majority of MMA champions have extensive Muay Thai training and experience.