The Czech Republic international penned a three-year deal with the north London side after the Gunners struck an £11m deal with the Premier League champions for the goalkeeper.
I know inside it will be killing him having to sell one of his best players to a title rival
Cech spent most of the 2013/14 campaign playing second fiddle to Belgium number one Thibaut Courtois, prompting speculation that the 33-year-old would seek a move away from Stamford Bridge.
And Mourinho’s former assistant Clarke gave an insight into what he believes with the Blues manager’s emotions following the sale of the experienced shot stopper.
Clarke told talkSPORT: “For me, he is still one of the best goalkeepers in the world. He is a great signing for Arsenal.
“I do smile a bit when I see Jose’s comments because I know inside it will be killing him having to sell one of his best players to a title rival.”
Cech won four Premier League titles, the Champions League and Europa League during a 12-year stay at Chelsea.
The defending English champions have already signed Asmir Begovic in an £8m deal as a replacement for the Czech stopper.
Mourinho also snapped up Manchester United flop Radamel Falcao on a season-long loan deal from Monaco.
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