The Italian, who coached Paris Saint-Germain to Ligue 1 victory last season, was unveiled as the Liga side's new manager on June 26 following the departure of Mourinho to Chelsea.
Following a campaign with only the Super Cup to show as silverware, Vialli believes that his compatriot is the right man to bring trophies to the Santiago Bernabeu.
"He is definitely a great coach, has plenty of experience, knows how to manage groups, individuals and motivate players," he told AS.
"He's the best coach Madrid could have brought in, for the reasons I explained earlier. This teams needs to play well and win, and he is a technician prepared to do both."
The 48-year-old, who played alongside Ancelotti at international level, also insisted that he is a hugely different trainer to Mourinho.
"Yes, he is another type of person," Vialli added. "That era [under Mourinho] is in the past, but now this is a new era and Ancelotti will forget all that. I think Carlo will give satisfaction to the Bernabeu."
Ancelotti will be hoping to improve on a second-place Liga finish behind Barcelona, a semi-final loss in the Champions League to Borussia Dortmund and a Copa del Rey final defeat to local rivals Atletico Madrid.