Wellens, 38, was appointed in October having been in caretaker charge - but was axed after failing to save the club from sliding into League Two.
The midfielder made more than 160 appearances for Rovers during two spells at Doncaster and has already been touted as a possible replacement for Darren Ferguson who resigned on Monday night.
He was put charge of the Latics after John Sheridan's sacking on 25 September and led them to 14 wins from 43 games in charge.
"While he was unable to guide us to safety after being appointed, it certainly wasn't due to a lack of professionalism and dedication on his part," said a club statement.
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"The club will look to appoint a new manager as soon as possible and will be making no further comment at this time."
Wellens won his first four games as caretaker and was subsequently given the job on a permanent basis, with former Manchester United midfielder Paul Scholes and ex-Netherlands international Clarence Seedorf also having been linked with the role.