Kirill will serve as interim patriarch until a larger church council is held within the next six months to pick Alexy's successor.
The appointment of Kirill is a move that could open the way for more co-operation with Catholics.
He is known for his forthright style of speech and heads the Church's department for
external relations. Most Russians see him as the public face of the Church, frequently appearing on television.
Kirill has had extensive contacts with the Vatican and churches around the world, making him relatively open to new ideas, but he is a controversial figure among conservatives, analysts say.
The main issues in choosing the new Patriarch will be church relations with the state and the Catholic Church. Kirill has been a reformer on both matters.
The Kremlin is seen as having strong indirect influence over the decision.
Patriarch Alexy II's funeral will be held on Tuesday, in the Christ the Saviour cathedral in Moscow.
The cathedral was demolished on Stalin's orders. The date in 1931 when authorities demolished the cathedral, December 5, coincides with the date of Alexy's death. Reconstruction of the cathedral was one of his triumphs as patriarch.
Alexy's body was to be taken to the cathedral on Saturday for three days of public viewing. Mourning services were held across Russia and in Orthodox churches abroad.
Patriarch Alexy died at his residence outside Moscow on Friday. No cause for his death was given but the 79-year-old patriarch had been sick for some time.
Alexy was an establishment figure who restored the authority of the church after decades of Soviet repression.
He died at a time when the Russian Orthodox Church had not yet determined its preferred status, as an institution closely allied with political authorities or a church more in tune with the Russian people.