The 25-year-old actor, who plays Artie Abrams in the Fox series, described Cory's "overwhelming kindness, humour and talent" in a touching post late last night (29 July).
Taking to Instagram where he posted a photo of the pair on set, Kevin said: "So thankful that I and so many of you got to experience Cory's overwhelming kindness, humour and talent.
"There will not be a day that goes by that I won't miss him. Thank you all for your incredible support and patience."
Kevin's message came hours after Cory's co-star and girlfriend Lea Michele posted a heartfelt tribute and photo on Twitter.
Cory was found dead in his hotel room on 13 July in Vancouver, Canada. A coroner later stated that Cory had died from a heroin and alcohol overdose. Tributes have continued to pour in and a private memorial attended by cast and crew was held for the actor last week (25 July).
The memorial, in Hollywood, was a time to "share memories and music in an emotional celebration of the life of Cory Monteith," a statement from Fox to E! News revealed.
Glee will return to screens on 26 September for three episodes, one of which will be a special tribute to Cory who played the loveable high school quarterback Finn Hudson. The show will then take a hiatus while producers decide on its future.
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