The Frenchman underwent a liver transplant last year but did not have his contract renewed at Barcelona.
Abidal joins an impressive list of signings this summer for Monaco, which includes James Rodriguez, Radamel Falcao and Joao Moutinho.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.