The last campaign was a difficult one for the 33-year-old, having been displaced as first-choice goalkeeper at Stamford Bridge after 10 seasons.
Thibaut Courtois' promotion reduced Cech's game-time, leading to mounting frustration and speculation about the long-serving goalkeeper's future.
Mourinho was adamant that the Czech Republic international would not be going anywhere if he had his way, although Chelsea owner Roman Abramovich overruled the Portuguese and granted the long-serving goalkeeper the move he craved.
That £10million transfer to Arsenal went through on Monday and Cech is confident there is no ill-feeling between Mourinho and himself.
"I think it has been great to have a chat with Jose because he is a manager that I have worked with for the longest time in my career," he told Press Association Sport.
"He 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.
"He is one of the best managers in the world
Now, we will be opponents but it will not change our relationship, I believe.
"You know, 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," he added.
"He made his decision, I had to make my decision and obviously we're now in this situation.
"I have a huge respect for him and we had a good chat about it
Obviously I know he would have loved me to stay, but that's the way it goes."
Cech is clearly excited about the "new chapter" in his career, with his desire to impress part of the reason he is moving closer to the Gunners' north London base.
"Last season I realised that I am not in the phase of my career that I would be happy to be a back-up goalie and sit on the bench," he said, speaking in Prague.
"I believe that in all those games I played I showed that I still have the skills and the level required to play as a number one goalkeeper in the best league in the world, which is the Premier League.
"Obviously I am happy that I have this opportunity to start my new chapter with Arsenal
Hopefully I will have as much success as I had at Chelsea."
Cech rejected the notion that leaving Premier League champions Chelsea for Arsenal was a backwards step, pointing to their back-to-back FA Cup triumphs and the impressive way they ended the league campaign.
The quality of Alexis Sanchez, Mesut Ozil & Co also helps his argument, as does the desire shown by Arsene Wenger to kick on.
"We always said that if I had the permission from the club and from the owner to stay in the Premier League that I would consider every offer," Cech said.
"This is what happened and I have to say Arsenal came and put absolutely the best offer, in terms of the footballing side.
"They offered four years of the contract as well, which is a big commitment from them for a player who is 33 like me.
"That was a huge factor because everybody showed me that they want me to be a part of the club, a part of the team.
"I spoke to the manager and I have to say that Mr Wenger presented with the ambitions and the project which I am really glad that I can be a part of."
Cech could well begin life at Arsenal with a winners' medal as Wenger's side line-up in the Community Shield on August 2.
Standing in their way at Wembley is the club with whom Cech made 494 appearances, bringing with it understandably mixed emotions.
"Obviously I don't know how I am going to feel - it is hard to imagine," the goalkeeper said.
"But maybe playing the first game against Chelsea will be my advantage because then I will have that box ticked and I will be able to concentrate on the games then."
Source : PA
Source: PA