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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Who of Europe’s top strikers will move to England this summer?
After a dreadful start to their Bundesliga campaign, Borussia Dortmund appear to have weathered the storm after going five matches without defeat.