The England fullback crowned their victory over Wigan Athletic scoring the eighth goal himself.
Ex-Arsenal star Cole finally won a league crown with the Blues and expressed his hope the triumph might put an end to the criticism he has received.
He said: "It's my first title at Chelsea. I'm happy. Hopefully, now everyone will get off my back and realise why I came here.
"People say I haven't won a big one here. But now I hope it can be a great year and we can win the Double."