Benzema was in red-hot form, scoring 15 times in the competition and lifting the trophy for a fifth time in his career after the Spanish side beat Liverpool in the final.
Ancelotti became the first coach to win Europe's most prestigious club trophy four times. He first won the title with AC Milan in 2003 and 2007 before claiming it with Real in 2014.
England coach Sarina Wiegman was named the women's coach of the year after the Dutchwoman helped them win the European Championship on home soil, beating eight-times champions Germany in the final to lift their first major trophy.
Wiegman beat Olympique Lyon's Sonia Bompastor and Germany's Martina Voss-Tecklenburg to win the award.
"It's really nice to receive this great award, I'm very honoured and humbled," she said.
"This award is really for everyone involved with the England team, the FA, the staff and of course, most of all, the players. Thank you very much."
Barcelona's Alexia Putellas won the women's player of the year, beating England's Beth Mead and Germany's Lena Oberdorf to the top prize.
Putellas, who won the award last year along with the Ballon d'Or, netted 34 goals for Barcelona last season as the club won all the domestic trophies and reached the Champions League final.
The 28-year-old did not play in the Euros after tearing her knee ligaments in training.