The former United States boss became the first American ever to manage in the English top flight after leaving French outfit Le Havre. He succeeded Francesco Guidolin but spent a total of just 85 days at the Liberty Stadium.
Bradley won only two matches during his ill-fated stint in South Wales which included a chaotic 5-4 defeat of fellow relegation candidates Crystal Palace and a 3-0 win over Sunderland. He also drew two and lost seven, a run that saw his hapless side concede no fewer than 29 goals. A 4-1 home loss to West Ham United on Boxing Day proved to be the final straw, with Swansea left 19th and four points adrift of safety.
"We are sorry to lose Bob after such a short period of time," said 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.
"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.''
Bradley remained defiant following that drubbing by West Ham, but his departure seemed almost inevitable with frustrated supporters making their feelings regarding his management abundantly clear.
First-team coach Alan Curtis, who briefly took the reins as interim manager following the dismissal of Garry Monk in December 2015, has been placed in temporary charge alongside Paul Williams. The latter joined Bradley's backroom team on a two-and-a-half year contract in November six months after leaving Nottingham Forest.
Swansea intend to "update supporters on the search for a new manager in due course", although Giggs has emerged as the early bookmakers' favourite. The former Welsh international was overlooked following Guidolin's departure, but has remained out of work since ending his 29-year stint at Old Trafford following the arrival of Jose Mourinho in July.
Wales boss Chris Coleman could also be in the frame, while Gary Rowett and Alan Pardew have both been mentioned as possible candidates following their respective sackings by Birmingham City and Crystal Palace.
Troubled Swansea, who have now dismissed three managers in the space of just 12 months, close 2016 with a home clash against Eddie Howe's Bournemouth on New Year's Eve. They then face Crystal Palace and Arsenal either side of an FA Cup third-round tie against Hull City.