The Aussie actor's body was reportedly found by police Sunday after a welfare check was requested in a suburb of Sydney. His cause of death hasn't been announced, but cops say foul play isn't suspected.

Brummer's family released a statement, saying ... "We lost our handsome, talented, funny, complicated and beloved Dieter on Saturday morning." They add, "He has left a massive hole in our lives and our world will never be the same. Our thoughts go out to all of you who knew him, loved him, or worked with him over the years." They also asked for privacy.

Dieter's mostly known for his role as Shane Parrish on the Australian soap, on which he starred for several years in the '90s ... more than 500 episodes.

He'd done some other work since -- including roles on shows like "Underbelly," "Neighbours" and "Winners & Losers," among other small, one-time appearances -- but "Home and Away" is by and far his biggest claim to fame. It doesn't appear he'd acted much since about 2014.

Brummer was 45.