The former Chelsea manager signed Begovic from Stoke in 2015 - albeit Mourinho only lasted until December that year - Guus Hiddink taking charge of the Blues before Antonio Conte was appointed.
Begovic featured just twice last season in the Premier League and has now joined Bournemouth, where it is likely he will be the first choice goalkeeper.
Despite Conte leading Chelsea to top flight glory, the 30-year-old was under no illusions when it came to which manager he rated best, reports Football 365.
“I think the best manager I’ve worked under – and it was a shame it was for such a short time – was Mourinho.
“The way he thinks about the game, the way he works with players was incredible to see. Obviously be brought me to Chelsea so I’m grateful to him for that.
“I was lucky to play under many good managers but I would definitely put him on top of the pile. I learned a lot from him in the short space of time we worked together.”
Conte put to bed any speculation of him exiting Stamford Bridge last week when he signed a two-year contract. And Begovic feels the ex-Juventus boss arrived at the right time for the club.
“Conte was good. He was very intense, very intense with his work, very driven in his structure and his way of playing,” said Begovic.
“I think that’s what we needed after a year of turmoil. It was important to buy into the philosophy as a team and the structure. That’s what we did.”
Begovic says his farewell with Conte was brief and was ready for a new challenge in his career.
“It was very quick. ‘Good luck’. I wished him all the best, it was simple as that,” Begovic said.
“We had a couple of conversations but he left the decision up to me. He respected my wishes to want to achieve a new challenge. He was respectful of that.
“There was not much pull from him. I did my bit and was professional there and played my part. It was time to move on.