Head coach Rob Baxter said the former Australia lock's decision sends a warning to the rest of the Aviva Premiership not to try to poach the Chiefs' top stars.
Mumm, 29, joined Exeter in the summer of 2011 from the New South Wales Waratahs, assuming the captaincy from Tom Hayes at the start of this season.
Exeter have risen quickly through the Aviva Premiership ranks since their 2010 promotion a nd Baxter believes securing talismanic figures like Mumm to a new deal will help their fast-developing youngsters see their long-term future at the club too.
Baxter said: "He's been a fantastic signing for us since he turned up at the club in a lot of ways.
"I've spoken to a lot of people since he's taken over the captaincy and what a good job he's done, but first and foremost you've got to pin your place down as being a front-line player and he's done that.
"While he's been at the club he's grown into one of the real leaders within the side.
"From our perspective it's a really important signing for us.
"He's been one of the form locks in the Premiership I think and he's a stand-out performer for us every week."
Baxter added: "It's a really good signing and shows where we want to be heading as a team and the quality of players we want to attract to Exeter, and keep here as well.
"It's a compliment to the players that we want to move early to sign them up and it's a compliment to us that they're keen to get these things done early and stay."
Highly-rated duo Ian Whitten and Jack Yeandle, whose contracts were set to expire next summer, have already confirmed new deals.
Baxter expects more to follow suit in the coming weeks, while Mumm admitted it was an "easy decision" to extend his Exeter stay for another two years.
"I'm delighted to be staying with the Chiefs," said Mumm. "The deal, to be honest, was pretty easy to sort.
"All Rob needed to know was that I wanted to be here and likewise all I wanted to know was that he wanted me here.
"That was pretty much agreed straight away and then the rest was sorted very quickly."