The club confirmed the news on Twitter as well as on their official website.
The official Tweet read
The official statement from Swansea City read: "Swansea City can confirm that the club has parted company with manager Francesco Guidolin.
"He will be replaced by former USA national team manager Bob Bradley with the club having agreed his release from French club Le Havre after their fixture with Sochaux tonight.
"Three members of Guidolin's backroom team - Diego Bortoluzzi, Gabrielle Ambrosetti, Claudio Bordon - have also been released."
Speaking about the deal, club chairman Huw Jenkins said: "We are obviously disappointed to part company with Francesco.
"We felt he deserved his opportunity after the work he did last season. Unfortunately, we have not been able to carry performances over from last season and we felt we needed to change things as soon as possible in order to move forward in a positive way.
"We would like to thank Francesco and his staff for their services to the club and wish them well for the future."
On Bob Bradley's appointment, Jenkins added: "We are delighted Bob has agreed to join us. He is highly regarded as a coach and has a wealth of experience on the international and domestic front.
"He is well aware of the club's footballing philosophy and will provide us with strong leadership qualities and a renewed belief to compete at this level.
"It is never easy changing managers, but we are looking at a long-term appointment and we are confident Bob can settle us down and stabilise matters on and off the pitch."
Bob Bradley was in charge of the USA national team from 2006 to 2011 and was also in charge of the Egyptian national team.