The 46-year-old actor apparently died of a drug overdose. Envelopes containing what was believed to be heroin were found with him.
The stage-trained actor's rumpled naturalism brought him four Academy Award nominations - for The Master, Doubt, Charlie Wilson's War and Capote, for which he won. He also received three Tony nominations for his work on Broadway, including for Death Of A Salesman.
He was as productive as he was acclaimed, often appearing in two or three films a year while managing a busy life in the theatre.
Hoffman spoke candidly about his past struggles with drug addiction. After 23 years sober, he admitted in interviews last year to falling off the wagon and developing a heroin problem that led to a stint in rehab.
His family called the news "tragic and sudden". He is survived by his partner of 15 years, Mimi O'Donnell, and their three children.
Mike Nichols, who directed Hoffman in Charlie Wilson's War and Death Of A Salesman, said: "No words for this. He was too great and we are too shattered."
Kevin Costner said: "Philip was a very important actor and takes his place among the real great actors. We are left with the legacy of the work he's done and it all speaks for itself."
Comedian and actor Steve Martin praised Hoffman's 2012 Broadway performance in Arthur Miller's Death of a Salesman.
He said: "Shocked to hear of Philip Seymour Hoffman's death. If you missed him as Willy Loman, you missed a Willy Loman for all time."
Hollywood star Jim Carrey said: "Dear Philip, a beautiful beautiful soul. For the most sensitive among us the noise can be too much. Bless your heart."
Actor Steve Coogan added: "He did some tremendous work."