Williams has agreed a one-year deal with Toulon, where he will form a formidable second row combination with the South African lock Bakkies Botha.
Kennedy initially found life difficult after joining Toulon from London Irish last summer but he eventually forced his way into the side and played in the 16-15 Heineken Cup final triumph over Clermont Auvergne.
Although Kennedy felt that victory ultimately justified his move to France, he handed in a transfer request which was accepted by the club's owner Mourad Boudjellal.
"We did not want to keep a player against his will," said Boudjellal.
"If the desire is not there, it is useless to hold someone against their will."
Harlequins, who were hit by the unexpected retirement of lock Olly Kohn last week, and London Irish could both be in the market for Kennedy if he decides to come back to the Premiership.
Williams, who won 77 caps for the All Blacks and was part of their Rugby World Cup-winning side in 2011, joins a stellar cast of new recruits at Toulon that includes Martin Castrogiovanni, Drew Mitchell and Bryan Habana.
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