After a fantastic campaign that saw him win the Champions League at club-level and reach the World Cup final with Croatia, Modric won out the vote by a sizeable margin.
Lokomotiv Moscow, seeded in the top spot as Russia's champion, will play Porto, Schalke and Galatasaray in Group D.
Elsewhere, Cristiano Ronaldo will get the opportunity to face his "beloved" Manchester United as they were placed in the Group H with Juventus. For strikers, Ronaldo, now with Juventus, scored 15 goals in the Champions League last season, guiding the club to its third straight UCL title.
There were 13 former champions in a draw that included three teams - Hoffenheim, Red Star and Young Boys - making their group-stage debuts in the 27-season Champions League era.
Ronaldo, who completed a £90million move from Real Madrid to Turin this summer, spent six seasons at United and is regarded as one of the club's greatest ever players. "He really deserves the award than Ronaldo and Salah because he was very consistent", Akonnor said.
"I think the English teams are the best now in the world in terms of quality", said Crespo following the competition's group-stage draw. "That's definitely the case with Barcelona", Tottenham's Eric Dier told his club's website.
It is bound to be yet another tough year for Project Neymar in Europe after Paris Saint Germain was drawn into one of the toughest groups in UEFA Champions League 2018-19.
Changes brought in for this season mean half of the places in the group stage were allocated to the top four sides in the four best-ranked leagues: Spain, England, Germany and Italy. Red Star Belgrade is also in this group.
Matchday 1: Ajax vs. AEK Athens and Bayern vs. Benfica.
Group F: Manchester City, Shakhtar Donetsk, Lyon, Hoffenheim.
"I am not saying we will not try to win, but I don't want to put too much pressure on our team when Euro 2020 is the next big thing that counts".