The deal was announced at Old Trafford in the presence of new manager David Moyes and members of the United squad, who are concluding their preparations for their pre-season tour of Asia.
Manchester United's group managing director, Richard Arnold, said: "This announcement marks the club's first commercial venture in Russia, an expanding market we are keen to explore further.
"The club has close to 18 million followers in Russia, demonstrating the partnerships potential audience in the country.
"Aeroflot is celebrating its 90th birthday this year, but has already impressed us with its youthful energy as one of the youngest fleets in Europe."
Aeroflot have followed Russian energy giants Gazprom, the UEFA Champions League sponsors, into the lucrative European football market.