The goalkeeper signed a long-term deal with the north London club on Monday after being heavily linked with a transfer to Emirates Stadium from the Stamford Bridge club.
Chelsea’s decision to let the 33-year-old leave the west London outfit and join their rivals after 11 years at the club raised some eyebrows.
However, Mourinho stands by his decision and praised Cech for being such a loyal servant to Chelsea over the years.
Mourinho told Chelsea’s website: “Petr has been a great servant for Chelsea for 11 years and helped this club to win almost everything there is to win.
“I always said I wanted him to stay but I understand Petr needed to move on to play first team football every week. Sometimes you have to respect the wishes of someone who has earned so much respect with his service and actions for your club. I support the owner’s decision to honour the player in this way.
“It is very rare in football to make a decision like this and for that reason I am proud of my club for making it. There are not many clubs in the world big enough to be able to make that decision.
“Petr’s success at this club will always to be remembered and we thank him for everything he did.”
The goalkeeper, who fell behind Thibaut Courtois in the pecking order at Stamford Bridge last season, has more than 114 caps for the Czech Republic and joined Chelsea from Rennes back in 2004.
Cech has already passed his medical with the Gunners and will join up with his new team-mates shortly to begin preparations for the 2015-16 season.
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