The Swans were 16th in the Championship when he arrived, having taken 11 points from seven games under Sheehan during his previous spell as caretaker boss, which came following the sacking of Michael Duff in December 2023.
Despite some difficult days in the early part of his tenure, Williams led Swansea to a 14th-placed finish last May and set out this season hoping to make steady progress while developing the young players in his squad.
He was on course to achieve those goals until the collapse in 2025 which has prompted his exit.
Williams goes just as Richard Montague, who he worked with at Notts County, takes up the role of director of football at Swansea.
Williams felt Montague’s arrival would assist Swansea’s off-field operations, having been critical of the club’s failings in the mid-season window.
After Blackburn, Swansea have 10 days without a fixture before they go to Preston on 4 March.
“We will keep supporters informed of developments when we are in a position to announce a new head coach, while Alan, his staff and our squad focus on our upcoming fixtures,” Coleman added.
Swansea, meanwhile, have postponed a much-anticipated fans’ forum which had been due to take place on Tuesday, 18 February until Monday, 3 March.
Williams and Coleman had been due to answer supporters’ questions at the event, but Swansea say they have put it back as a result of Williams’ exit.