The Blues activated a release clause in the France international's contract.
He was available for £8.5m, but Arsenal appeared on the scene to offer him first team football in North London.
Remy decided to join Chelsea because they offered better wages, even though he could simply be a squad player at Stamford Bridge.
He arrives at The Bridge as Fernando Torres departs, with the Spain frontman having gone to Italy to join AC Milan on a two-year loan.
He refused to sign for Newcastle on Friday.