Smith, who has a record of 103-68 over five seasons with the Golden Gophers, took the team to the National Invitation Tournament championship game last season after compiling 23 wins.
The extension runs through the 2016-17 season.
"Tubby took over our program at a difficult time and quickly got it headed back in the right direction, both athletically and academically," Teague said. "Since then, Gopher basketball has continued to make strides under his leadership with four post-season appearances, including last year's exciting run to the NIT title game."
"I am focused on reaching our full potential as a program," Smith added. "That is why we came here five years ago and it is still our goal."
Smith, who has led Minnesota to two NCAA Tournament berths and two NIT appearances, has a 490-213 career record a through 21 seasons with Tulsa, Georgia and Kentucky and Minnesota.