Edwards has committed his future until the summer of 2023 following speculation linking Tranmere, Wigan and Fleetwood with interest in the centre-back.
The 27-year-old arrived at Tannadice from Blackpool last summer, making 33 appearances, and was keen to extend his stay with Tam Courts' side.
"I'm buzzing to get this new deal done," he told United's website. "My time at United so far has been brilliant. It's the best group of lads I've been with in my career both on and off the pitch, it was a no-brainer to want to stick around.
"We finished last season a point outside the top six and a cup semi-final, this is a club that's going places and I want to be part of that. You also see the fans getting back in Tannadice last night and the atmosphere that brings, so I can't wait to see the place packed out.”