Bradley replaced Francesco Guidolin in October but the Swans have won just twice following his appointment.
American Bradley replaced Francesco Guidolin in October but the Swans have won just twice following his appointment and lie second from bottom in the table.
"Swansea City can confirm that the club has parted company with manager Bob Bradley," the Welsh side said in a statement.
His departure comes a day after Swansea were thumped 4-1 at home by West Ham, the club's seventh defeat in Bradley's short-lived tenure.
"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 told US broadcaster NBC Sports.
"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."
The 58-year-old Bradley took training on Tuesday but was subsequently relieved of his duties, less than three months after taking over.
"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."
Jenkins added: "Personally, I have nothing but praise for Bob. He is a good man; a good person who gave everything to the job. His work-rate is phenomenal and we wish him well for the future."
First-team coaches Paul Williams and Alan Curtis will take over from Bradley on an interim basis as the club searches for a new manager.
Bradley, who managed the US national team at the 2010 World Cup, became the first American boss in England's top flight after he was appointed in place of Guidolin, an Italian.
Bradley was also Egypt coach before stints in Norway and France with Stabaek and Le Havre. He left the latter to take the top job at Swansea having narrowly missed out on promotion to the French top division last season.
Swansea's next match is against Bournemouth at the Liberty Stadium on Saturday.
The Swans are four points from safety and above last-place Hull only on goal difference.