Suker played a key role in Croatia's third-place finish at their first World Cup as an independent nation in 1998, ending up as the tournament's leading marksman with six goals.
He also played in Real Madrid's triumphant Champions League team that year, making a brief substitute appearance at the end of their final victory over Juventus.
The 47-year-old, president of the Croatian FA since 2012, also had spells at Sevilla, Arsenal and West Ham United and joins fellow former professionals Michel Platini of France, Angel Maria Villar of Spain and Borislav Mihaylov of Bulgaria on the committee.
Platini was re-elected UEFA president earlier on Tuesday.
David Gill of England, already a member of the executive committee, was also elected as UEFA's British vice-president on FIFA's executive committee after beating Trefor Lloyd Hughes of Wales by 43 votes to 10.
He will replace Jim Boyce of Northern Ireland who retires after the FIFA Congress in May.
The election was a first because previously only the four British associations voted for their vice-president but from now on it will be decided every fourth year by all 54 member nations.
Former Manchester United chief executive Gill was the third European vice-president elected to FIFA on Tuesday.
He followed Platini, who continues as a FIFA vice-president in his role as UEFA president, and Villar who was re-elected to the position he already held.
The final European position on the FIFA executive committee was filled by German FA president Wolfgang Niersbach, a former sports journalist.
He replaces compatriot Theo Zwanziger who is retiring in May.
(Editing by Tony Jimenez)
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