The 46-year-old was found dead in the bathroom of his apartment at 11.30am local time (4.30pm GMT) today.
Awarded a best actor actor Oscar for his role in the 2005 film Capote, Seymour Hoffman checked into rehab in May for heroin use.
"He was found dead in his bathroom of an apparent drug overdose," an NYPD spokesman said.
Police were called to 35 Bethune Street in the West Village area of Manhattan by a friend of the actor, the spokesman said.
The Office of Chief Medical Examiner will investigate the exact cause of death.
Seymour Hoffman had admitted to struggling with drug addiction in the past but had reportedly been clean for 23 years before a relapse last year.
"I went to rehab, I got sober when I was 22-years-old," he said in a 2006 interview. "You get panicked... and I got panicked for my life."
Tributes quickly poured in for the actor, who was working on the last instalment of the dystopian adventure franchise The Hunger Games, in which he played the role of head game maker Plutarch Heavensbee.
Actress Mia Farrow wrote on Twitter: "OH NO!!!!! Philip Seymour Hoffman has died. A truly kind, wonderful man and one of our greatest actors - ever."
She added: "Rest in peace Philip Seymour Hoffman. We who marvelled at each of your performances are grateful and very very sad."
John Hurt - who starred with Seymour Hoffman in 2003 film Owning Mahowny - was among the celebrities left shocked by the news on the red carpet at tonight's London Critics' Circle Film Awards in central London.
"It's a devastating loss. His contribution was massive," he said.
12 Years a Slave director Steve McQueen commented: "I'm a huge admirer. How sad and tragic. I feel for his family."
Steve Coogan said: "He did some tremendous work. Everything he was in he raised the quality of his film just by his presence.
"People have different opinions about actors but you wouldn't find anybody who would have a bad word to say about any of his performances, they were all incredibly nuanced."
Skyfall actress Naomie Harris said: "That's a huge loss for everyone.
"He was an extraordinary and intelligent man, so it's incredibly sad, and it makes the evening all a bit more sombre now, having heard."
Comedian and actor Ricky Gervais posted on Twitter: "Such shocking & sad news. RIP Philip Seymour Hoffman. One of the greatest actors of a generation and a sweet, funny & humble man."
US actress Whoopi Goldberg wrote: "A truly great actor... Gone.. I hope someone says hey whoop it's a hoax.. R.I.P."
A spokesman for the British Academy of Film and Television Arts said: "We're shocked and deeply saddened to learn that Philip Seymour Hoffman has died."
The news of Seymour Hoffman's death came after claims that his representatives had denied a death hoax spread earlier in the week.
Born in Fairport, New York, in 1967, Seymour Hoffman got his first acting role in a 1991 episode of long-running police show Law and Order.
He went on to play memorable characters in films such as The Big Lebowski, Boogie Nights and Magnolia and also had a distinguished career in the theatre.
The actor leaves behind his long-standing partner and costume designer Mimi O'Donnell and their two daughters and son.
Seymour Hoffman's family said in a statement: "We are devastated by the loss of our beloved Phil and appreciate the outpouring of love and support we have received from everyone.
"This is a tragic and sudden loss and we ask that you respect our privacy during this time of grieving. Please keep Phil in your thoughts and prayers."