The 35-year-old former Real Madrid defender has agreed a 12-month deal with the newly-promoted Ligue 1 side, joining Joao Moutinho and James Rodriguez in signing for the club
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Carvalho told the official club website: "I'm very happy to join Monaco and to be part of the new adventure. This is a new challenge for me."
The newly-promoted Ligue 1 side backed by Russian billionaire Dmitry Rybolovlev are also close to finalising a deal for Atletico Madrid striker Radamel Falcao, who has passed a medical on Tuesday, and Barcelona goalkeeper Victor Valdes is reportedly close to sealing a move.
Carvalho was in the Champions League-winning Porto side which beat Monaco 3-0 in the 2004 final.