Mourinho wished Ancelotti, who he described as his best friend, good luck against Liverpool when they battle at Stade de France on May 28.
Tammy Abraham’s early headed goal was enough to earn the Italians a 2-1 aggregate win after drawing the first leg at the King Power Stadium.
Roma will now take on Feyenoord, who beat Marseille 3-2 on aggregate in the second semi-final game.
The final comes up in Tirana, Albania on May 25, the club’s first major European final since 1991.
Ancelloti and his Real Madrid side will have a date with Liverpool in the final of the Champions League after Los Blancos recorded a stunning comeback against Manchester City on Wednesday night.
During his post-match interview with Sky Sport Italia, Mourinho paid tribute to Ancelotti and is hoping that both of them emerge victorious at the end of the month.
Speaking after Roma’s win over Leicester, Mourinho said, “If you allow me a message for a coach who is my friend, the great Carletto, let’s both go and win the finals!”