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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?