In a statement Rehman said: "It is sad to be leaving Bradford City as I have very fond memories of the club.
"I would like to thank the chairmen, directors, players, management staff and fans."
The Pakistan international joined Bradford in 2009, originally on loan in January, before he agreed a full-time deal that summer, and made 71 appearances for the League Two club.
However he aired his dismay at being dropped to the bench in favour of young loanee defenders during a live interview on BBC Radio Leeds' West Yorkshire Daily programme.
That led to manager Taylor stripping Rehman of the club captaincy and placing him on the transfer list, which has resulted in the player's move to the Thai champions.
"I met the club officials over the weekend and my gut feeling was to sign.
"I have been made to feel very welcome by everyone and there is an extremely professional set up, excellent training facilities, 25,000 seater stadium and very passionate fans.
"I had offers from other clubs both here and abroad but Muangthong United made me a great offer and expressed the strongest interest in signing me.
"They want me to help them continue their impressive run of winning the Thai Premier League for a third consecutive year and further progress in the Asian Champions League."
Source: BBC Sport
Source: BBC Sport