The 31-year-old will join the principality club in a cut-price deal six months before his contract at Stamford Bridge expires in the summer, according to ESPN's Liam Twomey.
Blues staff anticipates the Spaniard will start Saturday's FA Cup third-round clash with Championship outfit Nottingham Forest in what will be his 198th and final competitive game for the west Londoners, Twomey adds.
The midfielder appeared to wave goodbye to the Stamford Bridge crowd at the final whistle after coming on as a substitute in the goalless draw with Southampton on Wednesday.
He now looks set to link up with his former Arsenal teammate Thierry Henry at Monaco. The French club is thought to have offered a contract running until the summer of 2022 as it looks to spark an upturn in what has thus far been a disappointing season.
Chelsea boss Maurizio Sarri recently spoke of his admiration for Fabregas and his hope to see the Catalonian stay at the Bridge.
"In this position, we have only two players, Jorginho and Fabregas, so for me, it would be really a problem without Cesc," the Italian boss said last week.
"I want him to stay, I don't know the final decision of Cesc and the club of course. But for me, it's very important and if Cesc will go I think that we need to buy another player, and it's not easy because, technically, Cesc is a very important player. And I think that in the market it's very difficult to find a player with his characteristics."
However, the club was ultimately unwilling to deviate from its policy of only offering one-year contract extensions to players aged over 30, meaning Fabregas, a two-time Premier League winner with the Blues, sees his future on the continent.
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