The 28-year-old Bogomolov was born in Moscow but moved to Mexico with his family when he was nine and then to the United States in 1992.
He has represented the US since turning professional in 2002 but has never played in the Davis Cup. At No 36, he is the fourth highest ranked American player.
His father, Alex Bogomolov, is a renowned tennis coach in the former Soviet Union, who coached Yevgeny Kafelnikov and Andrei Medvedev among others.
"It was my dream (to play for Russia) and I want to finish my career playing for Russia," Bogomolov said on Tuesday after winning his first-round match at the St. Petersburg Open.
Russia play Austria in the first round of next year's Davis Cup on February 10-12.
Davis Cup rules state that if a player is eligible to represent more than one country, the national association that wants to select him must apply to the International Tennis Federation six months before the match and await a ruling from the Davis Cup Committee.
The ITF said it received Russia's application on Bogomolov's behalf on Tuesday and will consider it at the next Davis Cup Committee meeting in December.