The former England international had asked to work both roles, but the Thailand Football Association did not accept his offer.
Worawi Makudi, the country's head of football said: "We have agreed to terminate the contract with Peter Reid as our national team coach.
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"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."
Reid was manager of the south-east Asian country for 13 games, of which he oversaw only two defeats, but his craving to return to coaching in the Premier League proved too strong.
The former Sunderland manager, who was photographed wearing the red and white of Stoke before his announcement, has left on good terms according to Makudi.
"I'm not disappointed, we have a good relationship. He did a good job for us but this is what he wants and he has a good future in the Premier League."
Stoke have not released a comment about Reid's appointment, although Pulis had gone on the record on the club's website last month to confirm his interest in appointing Reid as his deputy.
If Reid harboured any plans of one day returning to Thailand, he may have to reconsider, after the Thai press slammed his actions.
"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."