Mr Brummer played Shane Parrish in the popular Australian soap from 1992 until 1996.
A statement on the official Instagram page of the soap said: “Home and Away and @channel7 are deeply saddened to hear of Dieter Brummer’s passing.
“Dieter was a much-loved Home and Away cast member and celebrated by Australian and international audiences for his award-winning portrayal of Shane Parrish.
“We send our sincere condolences to Dieter’s family and friends during this very difficult time.”
On-screen, Brummer’s character Shane was married to Angel, played by actress Melissa George.
He also played Troy Miller in rival soap Neighbours and had roles in shows Underbelly and Winners And Losers.
Neighbours also shared a tribute to Brummer, with a post on Instagram reading: “Vale Dieter Brummer, joined the Neighbours alumni in 2012 as Capt Troy Miller.
“Our thoughts are with his family and friends.”
Home And Away star Georgie Parker, known as Roo Stewart in the soap, was among those paying tribute to Brummer.
She commented on Home And Away’s tribute, writing: “Such sad news, such a lovely man and a good actor too.”
A statement from the New South Wales police said: “About 1.30pm (Saturday July 24 2021), officers from The Hills Police Area Command responded to reports of a concern for welfare at a home on Glenhaven Road, Glenhaven.
“The body of a man was located inside the home.
“His death is not believed to be suspicious.
“A report will be prepared for the information of the Coroner.”