Abramovich, 42, who formerly served as the province's governor, was not present at the legislature's vote.
The Chelsea FC owner was elected a Chukotka Duma member on October 12, when a by-election was held to replace the chairman of the assembly, Vasily Nazarenko, who stepped down due to health reasons.
Reelected lawmakers and former deputy governors, Andrei Gorodilov and Aramais Dallakyan, were elected deputy Duma chairmen. Valentina Rudchenko was reelected deputy Duma chairperson.
Abramovich, ranked Russia's second richest man by Forbes, has been credited with funding major social projects in the sparsely populated gold and coal-producing region, which is about twice the size of Germany.
He pledged to continue to invest in the region despite resigning as governor in July. The president's nominee, Roman Kopin, was inaugurated as the new governor last Thursday.