Mumm was a member of the wider Wallaby squad in 2011 but wasn't required for Test duty despite featuring in all 10 domestic Tests the previous year and has now decided to join Exeter Chiefs instead of fight for his international place.
"He's a very good signing for us and a very good player," said Exeter boss Rob 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."
Mumm captained the mid-week Wallabies in the 2009 tour games against Gloucester and Cardiff Blues and has also skippered the Waratahs and Australia Schoolboys.
He featured in more than three quarters of the Tests played by Australia between his debut as a replacement against Ireland in 2008 and the end of 2010.
His move to Devon cements Rob Simmons' position as favourite to partner James Horwill in the Wallaby second row against the Lions and it also opens the door for the likes of Peter Kimlin to challenge for a Test spot given the retirement of Nathan Sharpe.