The former Monaco coach believes the Italian's man-management skills will see him perform better than his more confrontational predecessor at Santiago Bernabeu
Ancelotti replaced Mourinho at the helm prior to the start of the 2013-14 campaign after the Portuguese had left Madrid for Chelsea following a turbulent few months during which he reportedly fell out with a number of first-team players within the squad.
Simone believes that his compatriot's ability to deal with conflicts will prove to be vital in the Spanish capital and has backed him to perform better than Mourinho as a result.
"Ancelotti will definitely be a success at Madrid. Coaching Real Madrid is easy in one sense and difficult in another," Simone was quoted as saying by Marca.
"It's easy because you have players like Cristiano who, even if the system isn't working, can win you matches on their own.
"It's difficult because you've got to have what it takes to deal with a very tricky group. He knows how to handle the big egos you get at a club like Real Madrid.
"Ancelotti will have more success than Mourinho. I have a lot of time for Mourinho and I'm a big fan of his personality, but he finds it hard to back down once a conflict breaks out."
Mourinho guided Madrid to three domestic trophies during his three-year spell, although he was unable to steer them beyond the semi-finals of the Champions League.