The Real Madrid midfielder was crowned at the ceremony for the Champions League group stage draw on Thursday.
They face Paris Saint-Germain and Napoli, alongside Red Star Belgrade, who won the European Cup in 1991 and will participate for the first time in the modern, revamped Champions League.
Juventus' Portuguese forward Cristiano Ronaldo (C) outruns Lazio's Brazilian midfielder Lucas Leiva during the Italian Serie A football match on 25 August 2018 at the Allianz Stadium in Turin, Italy. Since then, only Liverpool came the closest to winning the prize, when they were dismantled by a rampant Gareth Bale, against Real Madrid.
Paul Pogba will also go up against his former team as United and Juve were drawn alongside Young Boys and Valencia, with the Spanish club tipped to cause some problems.
Monaco did not make it out the group stages a year ago after their 2017 semi-final, and Dortmund failed at the same stage. "He scored 15 goals, and carried Madrid on his back to win another Champions League.
Unai Emery answers journalist's phone during Arsenal news conference
They will fancy their chances as they host Emery's men, but the Spaniard will look to crash the party. I think he's got great vision and he's got some good players hasn't he".
There is no doubt about the victor, he is the best in his position".
"It's an incredible moment for me, I feel really excited and proud of this great award", said Modric.
"I expected a hard group, we have a hard group and that's what the Champions League is all about", Klopp told UEFA.
Modric - who was crowned UEFA Player of the Year for 2017-18 on Thursday - emerged as Inter's primary transfer target following the World Cup in Russian Federation but the Italian side have been unable to lure the 32-year-old midfielder to Milan.
Modric and his Real Madrid side face last season's semi-finalists Roma, CSKA Moscow and Viktoria Plzen.