"We are sorry to lose Bob after such a short period of time," said Swansea chairman Huw Jenkins. "Unfortunately things haven’t worked out as planned and we felt we had to make the change with half the Premier League season remaining.
"With the club going through such a tough time, we have to try and find the answers to get ourselves out of trouble."
Bradley, 58, saw his Swansea side pick up just two wins and two draws in his 11 games in charge, during which they conceded 29 goals, after he replaced Francesco Guidolin on Oct. 3.
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"I knew exactly what I was getting into when I came to Swansea and realised the hardest part was always going to be getting points in the short run," Bradley was quoted as saying on the Twitter feed of Sky Sports presenter Jim White.
"But I believe in myself and I believe in going for it.
"That's what I've always told my players. Football can be cruel and to have a chance, you have to be strong.
"I wish Swansea the best and look forward to my next challenge."
Former Manchester United and Wales winger Ryan Giggs is the early favourite for the job among the bookmakers, followed by Wales manager Chris Coleman, who used to play for Swansea.
Swansea's first team coaches Paul Williams and Alan Curtis will take charge while the club start looking for a replacement just days before the opening of the January transfer window.
American businessmen Jason Levien and Steve Kaplan brought a controlling stake in the Welsh club in June and Bradley was appointed after the sacking of Italian Guidolin, who had joined in January to replace ex-Swansea player Garry Monk.
Former U.S. national team coach Bradley became the first American to manage a Premier League club when he left French club Le Havre to take over at Swansea.
Having worked in American club football as well as in Norway and France, Bradley arrived with a wealth of experience but he was unable to turn the Welsh club's fortunes around.
(Writing by Ken Ferris in London; Editing by Alison Williams)
