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Ancelotti is off to become Brazil's national team head, while Modric is set to leave the club after next month's FIFA Club World Cup.

Madrid made a confident start at Santiago Bernabeu but was unable to make the breakthrough, with Mbappe forcing Unai Marrero into two smart saves.

The hosts were handed the chance to take the lead from the penalty spot in the 38th minute for a handball against Jon Martin, a decision confirmed after a video assistant referee (VAR) review.

Mbappe stepped up from 12 yards and saw his initial effort saved by Marrero, but LaLiga's leading marksman was on hand to tuck home the rebound.

Ancelotti's team continued to dominate proceedings after the break but without reward, with Ancelotti turning to his bench and introducing Vinicius Junior in the 55th minute.

The Brazilian combined brilliantly with Mbappe to seal the win seven minutes from time, with the Madrid talisman making no mistake as he tucked home his 31st league goal to cap a fine debut season in the Spanish capital.

Madrid finished the season with 84 points, one behind champion Barcelona, which plays Athletic Club on Monday (AEST).

Victory for Madrid capped a fitting end to both Ancelotti and Modric's time at the club, with the pair sharing an embrace at the full-time whistle.

Indeed, the Italian manager leaves Los Blancos as their most successful manager, having lifted 15 major trophies across his two stints with the club.

Modric, meanwhile, will still feature at the FIFA Club World Cup, but departs the club he joined back in 2012 as its ninth-highest appearance maker, turning out 591 times across all competitions, while scoring 43 goals and providing 95 assists across those matches.

But Madrid is in good hands with Mbappe, who became the fourth player in history to reach 30 or more goals in a debut LaLiga season, after Pruden in 1940-1941 (33), Romario in 1993-1994 (30) and Ronaldo Nazario in 1996-1997 (34).