Clement will not be in the dugout for Tuesday night's fixture against fellow strugglers Crystal Palace, with caretaker manager Alan Curtis set to take charge.
Clement, left, worked alongside Carlo Ancelotti at Chelsea, Paris St Germain, Real Madrid and Bayern Munich.
Clement, who many thought was unlucky to be sacked by Derby last February as he had led them to fifth place and were only five points adrift of then leaders Hull, has accrued an excellent reputation as a coach.
Gibbs has been confirmed as Clement's number two, having previously been Assistant head of coach and player development at Hotspur Way.
At the same time, it is easy to see why Swansea's board have always been impressed by Clement whenever their paths have crossed.
The 44-year-old had been working as Carlo Ancelotti's assistant manager at Bayern Munich but it was announced on Tuesday afternoon that he had signed a two-and-a-half year contract at the Liberty Stadium.
The ex-Derby manager has been given the top job by the relegation-threatened Swans.
Bayern gave Clement permission to hold talks with Swansea over becoming coach the day before. Counting to five has always been one of Ancelotti's ways of dealing with problems that could easily escalate.
Clement's playing endeavors were restricted to non-league level and he worked his way up in coaching from the bottom.
Curtis, one of Swansea's most celebrated players, said Clement had already made an impression with the players.
"But my real desire and ambition was to become a head coach again as quickly as possible, so I am absolutely delighted to be here at Swansea and a Premier League manager".