There were no signs of foul play, they said, and the cause of death was not immediately apparent.
Paramedics responding to an emergency call found Monteith, 31, dead at the Fairmont Pacific Rim Hotel in the city centre, Vancouver Police Department acting chief Doug LePard told a news conference.
Monteith had checked into the hotel on 6 July, and was due to check out on Saturday, LePard told reporters. Others were in the hotel room with Monteith on Friday night, but evidence including his fob key entries indicate he returned to his room by himself early on Saturday and was alone when he died, police said.
"We do not have a great deal of information as to cause of death," coroner Lisa Lapointe said.
Lepard said Monteith had been out with people earlier and that those people were being interviewed.
LePard said he wanted to offer condolences "to the family, friends, castmates and millions of fans of Mr Monteith".
Monteith's spokeswoman, Melissa Kates, said in a statement: "We are so saddened to confirm that the reports on the death of Cory Monteith are accurate."
"I have no words! My heart is broken," Dot-Marie Jones, who plays football coach Shannon Beiste on Glee, said on Twitter on Saturday night. She called Monteith a "hell of a friend" and an "amazing" man.
"What an absolutely tragic loss of a very talented young man," tweeted the actor Zooey Deschanel.
Fox and the producers of Glee, including 20th Century Fox Television, called him an exceptional performer "and an even more exceptional person. He was a true joy to work with and we will all miss him tremendously".
"We are in shock and mourning this tragic loss," his representatives at Viewpoint public relations in Los Angeles said in a statement.
In April, Monteith admitted himself to a treatment facility for "substance addiction" and asked for privacy as he took steps toward recovery, a representative said at the time.
Lea Michele, his Glee co-star and real-life girlfriend, told People magazine then she loved and supported him and was proud he was seeking help.
It was not Monteith's first time in rehab. He received treatment when he was 19 and had previously talked about his addiction struggles, saying he had a serious problem and took just "anything and everything".
He told Parade magazine in 2011 he was "lucky to be alive".
Monteith, who turned 31 on 11 May, starred in Glee as a high school football player who puts his status and popularity at risk to join the glee club and its outcast members.
The show, with its pop music-based song-and-dance numbers and high-profile guest stars including Gwyneth Paltrow, became an immediate hit and made stars of its relatively unknown cast.
On his Twitter account, Monteith described himself as "tall, awkward, canadian, actor, drummer, person".
Monteith was born in Calgary, Alberta, and moved to Vancouver Island as a child.
His TV credits included roles on the series Kaya and Kyle XY. His film credits included Final Destination 3, The Invisible, Deck the Halls and Whisper.
An autopsy was set for Monday, LePard said.
.jpg){kind=link}