His body was found on Sunday after a friend called emergency services. Police say he apparently died of a drug overdose.
Many fellow actors have been paying tribute to him.
Hoffmann made his name in the 1990s in films including Boogie Nights and the Big Lebowski, before winning the best actor Oscar for his 2005 portrayal of writer Truman Capote. Throughout his career Hoffman featured in independent films as well as Hollywood blockbusters such as Mission Impossible III. His latest role was in the Hunger Games series of films.
Hoffman's family called his death "tragic and sudden".
"We are devastated by the loss of our beloved Phil and appreciate the outpouring of love and support we have received from everyone," they said in a statement on Sunday.