The former Gunners manager also believes the keeper has been rewarded by the Blues for his loyalty.
At 33, he still has several good years in him and Arsene Wenger has moved quickly to secure his signature, in the process improving one of his side’s weakest areas with a top-class player.
And Graham believes Cech can still perform at the highest level in the Premier League for the foreseeable future.
“He’s still got a few more years left in him yet,” he told talkSPORT.
"Goalkeepers can last well into their 30s at the top level and he is a top level goalkeeper. Let’s be honest, apart from the last few seasons, Arsenal have always had really good, top class, goalkeepers and that’s very important if you want to win the big trophies.”
Loyalty at last
Cech’s impending move across London to Arsenal is something of a surprise, given that the big clubs generally do not do deals very often.
Indeed, the move comes as more of a shock considering that Jose Mourinho was thought to be less than keen on doing a deal with the Gunners, knowing it would be strengthening a direct rival considerably.
Graham though, believes the Blues will allow the transfer to happen as a reward for the goalkeeper’s loyalty to the side over the last decade and more.
"There is a bit of loyalty at last,” he added.
“Sometimes it doesn’t happen in the game but he’s been very loyal to Chelsea and he’s been outstanding for them now for more than ten years. Ideally [if you were Chelsea] you wouldn’t let him go but I think they’re rewarding him for his loyalty.”