Reid had asked to remain coach of the Southeast Asian country alongside his job as assistant manager at Stoke, but Thailand would not accept his proposal, Worawi Makudi said.
"We have agreed to terminate the contract with Peter Reid as our national team coach," he said in a telephone interview.
"He wanted to work in the Premier League at the same time but we told him it could not work that way. He could not do both, it's impossible."
Stoke were not immediately available for comment but last month manager Tony Pulis said on the club's website he was hoping to get clearance from the Thai Football Association to bring in Reid as his number two.
Worawi's announcement ends weeks of speculation about Reid's future as Thailand coach after he was quoted saying he craved a return to the Premier League, and was photographed wearing a Stoke City kit during a training session on holiday in England.
Reid's no-nonsense style and modern coaching methods earned him the respect of Thailand's talented but often undisciplined players, who suffered only two defeats during their 13 competitive games under the Englishman.
GOOD JOB
Worawi said the ex-Manchester City and Sunderland boss's departure was amicable and Reid was reluctant to leave.
"I'm not disappointed, we have a good relationship," said Worawi.
"He did a good job for us but this is what he wants and he has a good future in the Premier League."
Reid's assistant, Steve Darby, a former national development manager of Australia's football federation, will take over as caretaker coach, Worawi added.
Asked if Thailand would be looking to hire another foreign coach, Worawi said: "We will be looking into that in the near future."
Reid, who was hired to develop the Thai game and steer the team to the 2014 World Cup, will be sorely missed in Thailand after giving the team a major facelift.
However, his activities while in England and his refusal to comment on his future with Thailand left a sour taste in the mouths of Thai fans and the Kingdom's football-obsessed media.
"Even if Reid comes back to coach Thailand, the fans may find it hard to swallow," the mass-circulation Thai Rath newspaper said in a commentary last week.
"Reid working for Stoke without prior warning to the Thai Football Association was a slap in the face for the fans."
