There was no immediate word from Swansea but Sky Sports and the BBC said Clement had agreed a 2-1/2 year deal.
Swansea are bottom of the table after a dreadful run of form and face fellow strugglers Crystal Palace on Tuesday when caretaker manager Alan Curtis will take charge of the team.
Clement was formerly assistant manager at Chelsea and Real Madrid and was in charge of Derby County for eight months before he was sacked by the Championship club in February last year.
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(Reporting by Martyn Herman; Editing by Ken Ferris)
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