The tradition is that when a cardinal is made by the pope, the cardinal becomes a priest of the Diocese of Rome. As members of the Roman clergy, he receives a church, though now in title only, (which he vicarious takes care of by finding the funding for projects), and has the responsibility of entering a conclave to elect a new pope and when asked, to provide his consultation on certain topics.
The new cardinal will take possession of his new church within the next six months.
Interesting to note: Cardinal Antonios Naguib is not assigned a titular church because he uses Saint Paul outside the Walls because the church’s close, historic connection with the See of Alexandria; Cardinal Fortunato Baldelli is assigned the Benedictine church of Sant’ Anselmo (replacing the recently deceased Cardinal Mayer, OSB); Cardinal Raymond Burke is assigned Church of Sant’ Agata de’ Gotti, the church where the Stigmatine Fathers have the generalate (replacing the recently deceased Cardinal Spidlik, SJ); the 93 year old Cardinal Domenico Bartolucci is assigned the Church of Santissimi Nomi di Gesù e Maria in via Lata (replacing Cardinal Dulles, SJ).
The complete list of the assignments of the churches is here.