Withe, 59, previously coached the side from 1998 to 2002, leading Thailand to two ASEAN Football Championships and the semi-final of the Asian Games in Bangkok.
"Peter Withe is an interesting choice because we are very close friends and I was the one who asked him to coach the Thai team last time," Football Association of Thailand chief Worawi Makudi told Siam Sport.
Thailand have had a string of big-name British managers, including former Sunderland and Manchester City boss Peter Reid, who left in September 2009 after only one year.
The reasons for the departure of Robson, a former England and Manchester United captain, are unclear. He underwent surgery for throat cancer on March 3 and has previously said doctors were optimistic he would make a full recovery.
"Bryan wished to resign and his contract was terminated by mutual consent, but I cannot give any more details," said Worawi.
He denied the move was linked to an accusation last month by former English Football Association chief David Triesman that Worawi asked for broadcasting rights in return for his support for England's bid for the 2018 World Cup.
Worawi last month vowed to file a complaint against Triesman for defamation.
"This is not connected to Lord Triesman's case. The Thai Football Association hired Bryan Robson to coach our team. We pay him, not the English Football Association," Worawi said.
Robson won 90 international caps during a glittering career, including 65 as captain, despite a string of major injuries. England manager Sir Bobby Robson nicknamed his namesake "Captain Marvel".
But he had a patchy record with Thailand since taking over in September 2009, winning only seven of 18 matches.
Manchester United, who continue to employ Robson as an official club ambassador, said the 54-year-old former midfielder's recent treatment for throat cancer was not behind his decision to leave Thailand.
An announcement on his replacement is expected after the Football Association of Thailand's presidential election on July 17, at which Worawi is seeking re-election.