A dual European Cup winner as a player for AC Milan, Ancelotti also coached the Italian club to Champions League glory in 2003 and 2007, as well as the Serie A title in 2004.
He has also coached at Juventus, Parma and Reggiana, and enjoyed a successful stint with Chelsea, who he led to the Premier League-FA Cup double in 2010.
He has been a leading candidate to replace Mourinho since announcing in May that he wanted to leave the Parc des Princes after 18 months in charge.
A Real statement read: "Carlo Michelangelo Ancelotti will be the coach of Real Madrid next season.
"The Italian has experienced success in every country where he has managed and arrives in the Spanish capital after being named coach of the season in France.
"He has won practically everything in the ambit of international football (two Champions Leagues, two European Supercups, one World Club Cup and one Intertoto Cup) and has won the league in three distinct championships in which he has managed (Italy, England and France).
"Familiar with the pressure of managing big teams on the continent, the Italian is guaranteed to manage an exciting project."
Real president Florentino Perez's decision to hire the well-liked Ancelotti has been viewed as an attempt to replace Mourinho with a less confrontational figure.
Mourinho, who has returned to Chelsea, led Real to the La Liga title two seasons ago but his final term at the helm was marred by public disputes with members of the team.
His replacement at PSG is Laurent Blanc, who has signed a two-year deal, having been out of work since France were knocked out of Euro 2012 at the quarter-final stage.
A World Cup winner with France as a player in 1998, Blanc coached Bordeaux between 2007-10, leading them to Ligue 1 glory in 2009.
He will oversee the start of pre-season training next Monday and a club statement read: "The board of Paris Saint-Germain has given Laurent Blanc the mission to build on last season and to continue the club's ascendency towards the summits of the European game."
Tottenham boss Andre Villas-Boas, Mourinho, ex-England coach Fabio Capello and recently-appointed Napoli chief Rafa Benitez had all been linked with PSG.
However, the ambitious French outfit have plumped for Blanc, who enjoyed a distinguished career as a central defender which was crowned by his key role in the France side which won back-to-back major trophies at their home World Cup in 1998 and Euro 2000, eventually retiring with 97 caps and an impressive 16 international goals to his name.
He also collected league titles in France with Auxerre and in England with Manchester United, the European Cup Winners' Cup with Barcelona and domestic cup competitions with Montpellier, Auxerre and Barca.