Long considered a potential heir apparent to Los Angeles Lakers coach Phil Jackson, Rambis was lured away from Jackson's staff by a four-year deal believed to be worth in excess of $8 million.
Wolves owner Glen Taylor confirmed ESPN.com's report in an interview with the St. Paul Pioneer Press late Saturday, telling the newspaper that he expects Rambis to formally sign the contract Monday.
"Kurt, with his experience playing and coaching for a winning organization and working under people like Pat Riley, will bring a lot to our organization," Taylor told the Pioneer Press. "In meeting with him and talking to him, I know he's very excited about having an opportunity to help build his own team."
Sources told ESPN.com that the Wolves are planning a Tuesday news conference to introduce Rambis as the replacement to Kevin McHale.
New Minnesota president David Kahn said in a text message to The Associated Press he met with Rambis' agent Sunday but have yet to conclude the deal.
After turning down the Sacramento Kings' job during the NBA Finals, Rambis was chosen by Kahn from a group of finalists that also featured ESPN analyst Mark Jackson and Houston Rockets assistant coach Elston Turner.
Kahn interviewed more than a dozen candidates in a deliberate search that began after the NBA Draft in late June.
The Los Angeles Times first reported Wednesday that Rambis traveled to the Twin Cities to meet with a Wolves contingent that included Taylor, which appeared to signal that the 51-year-old was the choice to fill the league's only remaining coaching vacancy.
Minnesota hired Kahn in May after a 24-58 season and a protracted search for a new front-office chief that focused initially on San Antonio's Dennis Lindsey and Portland's Tom Penn.
Kahn has since been unafraid to take risks and took his time with big decisions, first announcing that he would put off the coaching search until after the draft and then selecting point guards Ricky Rubio and Jonny Flynn with the fifth and sixth overall picks.
McHale ended a nearly 15-year association with the franchise in June when -- despite the support of franchise cornerstones Al Jefferson and Kevin Love -- he declined to return as coach after being offered only a one-year contract to stay.
Unforgettably clotheslined by McHale in Game 4 of the Celtics-Lakers championship series in 1984, Rambis was the only Wolves finalist with NBA head coaching experience. Rambis coached the Lakers for the bulk of the lockout-shortened 1999 season, posted a 24-13 record before Jackson arrived for his first stint with the Lakers.
The Wolves have not made the playoffs since Kevin Garnett led them to the Western Conference finals in 2004. They have won just 46 games in the last two seasons and have changed coaches four times in the last five years.
Marc Stein is a senior NBA writer for ESPN.com. Information from The Associated Press was used in this report.