Elected for four years, Chaturvedi was the senior vice-president of the federation, and replaces Chautala, whose third term at the helm ended recently.
He is currently lodged in jail following his conviction in a teachers recruitment scam in Haryana.
The new president will have Dhanraj Choudhary as secretary-general and Mahinder Pal Singh as treasurer, the two other principal office-bearers of the federation.
Choudhary, who took over from Mool Chand Chouhan after his demise three years ago, is in his second term, while Singh, a first-timer, replaces BK Bawa, as treasurer.
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The elections were conducted by returning officer UK Bansal, a retired IPS officer, in the presence of government observer Rachna Govil and Indian Olympic Association representative Anandeshwar Pandey.
All office-bearers, including one senior vice-president, eight vice-presidents, four joint secretary and seven out of eight executive council members, were elected unanimously.
The posts of one senior vice-president and one EC member have been kept vacant as there weren't sufficient nominations.
They will be filled later with the due process of election.