The former United States
coach arrives at English Premier League club Swansea as a replacement for Italian Francesco Guidolin, who was relieved of his duties the same day.
Struggling Swansea, which lost 2-1 at home to Liverpool at the weekend and is one place above the relegation spots, turned to Bradley after failing to win since the opening day of the season.
The 58-year-old American moves to the Liberty Stadium from French second division club Le Havre, which he has been coaching since November 2015.
Guidolin, who was appointed by Swansea in January, had been under increasing pressure amid a string of disappointing results.
Recent speculation had seen both former Manchester United star Ryan Giggs and Bradley strongly linked with the job.
In a statement
on Swansea's official website chairman Huw Jenkins said he was "delighted" to have secured the services of Bradley, adding: "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."
Jenkins said he was confident that Bradley "can settle us down and stabilize matters on and off the pitch."
He added that Swansea was "obviously disappointed" to part company with Guidolin, whose departure was announced on his 61st birthday.
"We felt he deserved his opportunity after the work he did last season," he said.
"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.''