Ivanovic left Chelsea to sign for Russian side Zenit St Petersburg on transfer deadline day.
The Serbia international left Stamford Bridge after a successful nine year stint at the club.
During that time he played under nine different managers with Mourinho and Ancelotti among them.
Antonio Conte v Jose Mourinho: Chelsea managers' stats compared
Fri, December 16, 2016
Express Sport compares Antonio Conte's impressive start as Chelsea boss to Jose Mourinho's 2015/16 statistics
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Express Sport looks at how Chelsea manager Antonio Conte compares with his predecessor Jose Mourinho, 12 months after ‘The Special One’ was sacked at Stamford Bridge
Chelsea sold Branislav Ivanovic to Zenit on deadline day
Carlo Ancelotti was said to be more popular than Jose Mourinho at Chelsea
And the 32-year-old has praised Mourinho but insisted Ancelotti’s calmness made him popular in the Chelsea dressing room.
"They call Mourinho the Special One, and I think he is," Ivanovic told Russian website Sport Express.
"If you win, his trust knows no bounds. He will make you fulfil the potential you were not even aware of.
"Training was unique under Mourinho. He sometimes plays mind games with the press, but when it comes to the most important things, the matches themselves, he is always very serious.
Branislav Ivanovic played under Jose Mourinho at Chelsea
“If you want to play for Mourinho, you have to follow his demands.
"Mourinho helps to develop the best qualities — professional and personal. You can't be indifferent to him. You either love him or hate him. That's what makes him special. I am glad that I had a chance to work with him.
"Ancelotti is very different. If players had a choice, I guess they would prefer to spend the entire career with Carlo. He is very calm and takes all the negative aspects on him, allowing the players to be comfortable. The results are equally good with both coaches."
Mourinho won three league titles during two stints at Chelsea, with Ancelotti winning the Premier League in 2010.