Thursday's win caps off a stellar 12 months for the 32-year-old, who also won the Golden Ball for his performances in helping Croatia finish as runners-up at the World Cup in Russian Federation.
Modric adds the UEFA award to the title of Best Player at this summer's World Cup in Russian Federation, and must now be considered a strong candidate to break the Messi/Ronaldo stranglehold which has dominated the Ballon d'Or in recent years.
Ronaldo then spoke on Cristiano Ronaldo's arrival at Juventus. I am sure there is a reason why he couldn't come. "Hopefully we will see each other soon somewhere else", said Modric of his old colleague.
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But Modric, who also claimed the Golden Ball at the World Cup, won the most votes from coaches and journalists to seal the award.
"I always try to improve on what I did the previous season, because matching what Messi and Cristiano do by scoring 50 to 60 goals a year is very hard".
"I'm not happy. I'm extremely happy at Real Madrid and I want to continue at this club for several years", the Croatia captain said, as quoted by Marca.
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His clubmate Sergio Ramos was named best defender while Real shot stopper Keylor Navas won the best goalkeeper prize.
Galled at seeing Ronaldo miss out on the Player of the Year award, Aveiro shared a graphic on Instagram comparing the stats accrued by Modric in the Champions League last season to those of her brother.
"It's an incredible moment for me and I feel excited and proud of this great award", the midfielder told the crowd after being branded UEFA's best player for 2018.
Danish global Pernille Harder, of German club Wolfsburg, won the UEFA women's player of the year prize. The Champions League final takes place on Saturday 1 June, at Atletico Madrid's Wanda Metropolitano stadium.
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During and after the draw UEFA also crowned a raft of players as their outstanding picks of the season.