The 28-year-old forward will leave Super 15 side Waratahs at the end of the current season.
Chiefs head coach Rob Baxter has identified Mumm, who has 33 international caps to his name, as a key addition.
"He's a very good signing for us and a very good player," said Baxter. "We've been watching him since the start of the Super 15 season and not only is he a back five forward coming into his physical prime, he's also vastly experienced and a good leader.
"We've looked at lot at him and we believe he has got a lot of ingredients that we want him to bring to the club. Personally, I think it's a great credit to what the players have achieved this season - and where we are as a club right now - that a guy of that standing wants to come and play his rugby here in Exeter."
The New Zealand-born forward made his debut for the Waratahs in 2004, playing his first Super Rugby match three years later against the Lions.
Versatile enough to play in the back-row, Mumm - who has 32 caps for the Wallabies - is the fourth new arrival confirmed by the Chiefs for next season and he will join Doncaster duo Alex Brown and Jack Yeandle, as well as Ulster's Ian Whitten in moving to Sandy Park this summer.
Mumm, who has previously captained the Australian national team in 2009, featured in Saturday's 30-21 win for the Waratahs against the Melbourne Rebels.
"I'm looking forward to seeing him get over here and working with him," added Baxter. "The move for Dean has happened very quickly and we're delighted to have him on board."
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