Cech was Chelsea's first-choice for 10 years but lost his place to Belgium's Thibaut Courtois last season and joined Arsenal on Monday.
Mourinho said he would have preferred Cech, 33, to remain with Chelsea this season but with the player no longer number one choice and wanting a move, supports the decision.
He also thanked Cech for his part in the club's success.
"Petr has been a great servant for Chelsea for 11 years and helped this club to win almost everything there is to win," Mourinho told the club website on Wednesday.
"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," Mourinho added referring to Roman Abramovic.
"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."
Cech, who made his Chelsea debut under Mourinho in August 2004 and won three league titles under the Portuguese coach plus the FA Cup and League Cup, stressed their mutual respect.
"He (Mourinho) had to make his decision at the start of last season, I had to make my decision at the start of this season but I will always keep the best regards for him because I believe that we had so much success and so much respect for each other," said Cech.
"He is one of the best managers in the world. Now, we will be opponents but it will not change our relationship, I believe.
"I learned a lot from him and one of those things was that if you have to make a hard decision, you need to make sure that you do it if you believe it is the right choice."
(Writing by Ken Ferris; Editing by Greg Stutchbury)
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