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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.