Monteith had been dating co-star Lea Michele for over a year. According to her rep, Michele is "devastated" by the news of this loss.
"We ask that everyone kindly respect Lea's privacy during this devastating time," a rep for the actress told People.
The 31-year-old made a decision to enter himself into a rehab facility in March for substance addiction.
UPDATE: CNN has reported that Monteith died as a result of "a mixed drug toxicity, involving heroin and alcohol," according to the British Columbia Coroners Service.
"At this point there is no evidence to suggest Mr. Monteith's death was anything other than a most-tragic accident," the coroners service said in a statement, adding that no further details were available pending a full investigation.