"I am staying and couldn't be more excited about our future," Hoiberg said in a text message to ESPN.com on Thursday night.
Hoiberg had talked to Minnesota this week, according to sources.
The Gophers locked in on Hoiberg, who played and worked for the Minnesota Timberwolves, after they were spurned by VCU's Shaka Smart. Minnesota fired Tubby Smith on Monday.
Hoiberg, who is 62-39 in three seasons with the Cyclones, finalized the contract with Iowa State president Steven Leath and athletic director Jamie Pollard on Thursday night.
"I sincerely appreciate the support that President Leath and Jamie have given me. Ames is my home and Hilton Coliseum has given me countless memories as both a player and coach. I look forward to continue leading a program that Cyclone fans can be proud of," Hoiberg said in a statement.
Hoiberg, a former star player at Iowa State, has led Iowa State to back-to-back NCAA tournament appearances for the first time in 12 years. The Cyclones nearly made the NCAA regional semifinals last Sunday before Aaron Craft's late 3 led Ohio State past Iowa State 78-75.
The result did little to dampen the enthusiasm over the job Hoiberg has done at Iowa State, though.
The deal is nearly identical to the one that Pollard and football coach Paul Rhoads agreed to before last season.
Hoiberg and Rhoads are extremely popular figures in central Iowa, and both figure to stick with the Cyclones for years to come.
"Nobody is better suited to be our head men's basketball coach and we wanted to show he and his family, along with all Cyclone fans, that we are committed to keeping him in Ames for the long term," Pollard said.
Information from The Associated Press was used in this report.