The Spanish giants hope the former Paris St Germain manager will unite the dressing room, calm fans and local media, and re-establish Real as serious challengers to La Liga champions Barcelona.
"Familiar with the pressures of managing the great teams of the continent [Juventus, AC Milan, Chelsea and PSG] the Italian is guaranteed to direct an exciting project," Real said on their website.
Milan won the Champions League twice under Ancelotti, 54, who had been linked with the Real post since Mourinho's exit at the end of last season.
Ancelotti, who will be presented on Wednesday, asked to leave PSG but the move was reportedly held up until the French champions found a replacement.
PSG announced they had agreed a two-year deal with former France coach Laurent Blanc at the same time as Real made public their agreement with Ancelotti.
Spanish media have reported that Real will pay PSG around four million euros in compensation for the year of his contract he still had with the French club.
Mourinho led Real to a King's Cup and La Liga title in his three years in charge, but his final season was characterised by public disputes with players such as captain Iker Casillas and defender Pepe which divided fans into two camps.
The Portuguese left the club by mutual agreement and has returned to former club Chelsea.
One of the accolades for the incoming coach, from former Milan player Paulo Maldini, made particular mention of Ancelotti's handling of his players.
"Of all the coaches I have had, he [Ancelotti] was the one who managed the dressing room with the most serenity," Maldini was quoted as saying on the Real website.
"The secret of our success was his normality. He isn't one of those who works alone, and this shows great intelligence. For this reason he will win titles wherever he goes: with Milan, Chelsea or Real Madrid."
EXPANSIVE STYLE
Real reached the Champions League semi-finals three years in a row under Mourinho but finished the most recent campaign without major silverware. Real finished 15 points behind Barcelona in La Liga last season.
The world's richest club by revenue want to add to their nine European Cups. Ancelotti will be expected to provide the much sought-after 'Decima' (10th) and a more expansive style of play after the perceived caution of Mourinho's counter-attacking system.
He won the Champions League with AC Milan in 2003 and 2007, after also being a member of the Milan squad that won the trophy twice, and lifted the Club World Cup with the Italians.
With Milan he scooped a league title and a cup, the same with Chelsea in England, and he guided PSG to the French league title last season.
Ancelotti has long had a good relationship with Real president Florentino Perez. He praised Perez in a recent autobiography where he credited the construction magnate with saying: "Carlo, one day you will be my coach."
Among Ancelotti's immediate tasks will be to establish a working relationship with former France midfielder Zinedine Zidane. Perez is keen for Zidane to take
