While Chelsea have wanted Fabregas to stay, they offer only 12-month deals to players over 30. The player himself had demanded a longer term deal.
Chelsea boss Maurizio Sarri asked Fabregas to stay but he wants more first-team football having started just one Premier League game all season.
Former Arsenal star Fabregas had been determined to play stay for the early part of January in order to reach the landmark of 500 club appearances in English football.
He achieved that against Southampton in midweek and today's showing was match number 501.
Cesc Fabregas burst out in tears on his farewell Chelsea appearance (Image: BT SPORT)
Cesc Fabregas burst out in tears on his farewell Chelsea appearance (Image: BT SPORT)
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Fabregas' exit will save Chelsea a significant sum in wages as he is currently on around £160,000 per week.
His next destination is likely to be Monaco, who are managed by his ex-Arsenal team-mate Thierry Henry.
Henry is looking to reinforce his struggling side by bringing in Premier League reinforcements this January.