Bouriko has been CFO since October 2013 and was previously a board member and the deputy CEO of En+. Prior to this, she spent 16 years at KPMG in Russia and Canada.
Soloviev, meanwhile, will be replacing Russian billionaire Oleg Deripaska as president.
Bouriko's focus will be on reducing Rusal's environmental footprint, introducing modern technologies and facilitating an efficiency programme.