Incumbent president Arkady Dvorkovich was re-elected for a second term.
Five-time world champion Anand was part of Dvorkovich's team.
Dvorkovich received 157 votes as against 16 by his rival Andrii Baryshpolets. There was one invalid vote and five abstentions.
The elections to the world chess body were held during the FIDE Congress which is being conducted alongside the 44th Chess Olympiad.
Viswanathan Anand has won five world titles with the last being the world rapid title in 2017.
Ahead of the elections, Dvorkovich had spoken about having Anand on his team.
He said, “I am really proud to have Anand running for deputy president. He is a great person and a great personality. He has been a long-time friend.”