The move came three weeks after athletic director Chris Hill fired Jim Boylen following consecutive losing seasons. Krystkowiak, who was traveling Sunday, will be introduced Monday.
The 46-year-old Krystkowiak has been an assistant with the New Jersey the past eight months. He played for the Jazz in 1992-93 as part of nine injury-plagued NBA seasons after being drafted in the second round (28th overall) in 1986 by the Chicago Bulls.
"I'm excited for Larry," Nets coach Avery Johnson said. "We're going to be losing a man of strong character, solid family, really good basketball coach. [He] did a lot of nice things for us this year behind the scenes. So I really enjoyed working with him. We think this is a great opportunity for him. He talked about getting back to college and we think it's really good timing for him. So again, we're excited for him."
This will be Krystkowiak's fourth head coaching job.
He was fired in 2008 after going 31-69 in one-plus season coaching the Milwaukee Bucks. He also went 42-20 with a pair of NCAA tournament bids in two seasons at Montana, and was 37-16 with the Idaho Stampede in 2003-04, leading them to the CBA title game.
The hire is an important one for Hill, now on his third coach since Rick Majerus departed.
Hill gave Boylen a contract extension after a 2008-09 season that saw the Utes go 24-10 and win a share of the Mountain West Conference regular-season title. Because of that extension, Boylen is receiving a $2 million severance package.
Hill also hired Ray Giacoletti, but fired him four years ago after a 54-40 mark.
Neither could match the success of Majerus, a fan favorite and cult figure during 14-plus seasons at Utah. Under Majerus, the Utes qualified for the NCAA tournament 10 times, advancing to the Sweet 16 twice and the national championship game in 1998.
His overall mark before leaving for health-related reasons was 323-95, and crowds filled Huntsman Arena regularly. There were plenty of empty seats as the Utes went 3-5 at home in conference play this season.
It will only get tougher with the Utes jumping to the Pac-12.
Asked if moving to a major conference would be a problem for Krystkowiak, Johnson said, "It's a bigger problem, but it can also be a big reward," he said. "That will not only be exciting for them from a basketball point of view, but for football also.
"I wouldn't focus on the big problem," Johnson said. "I would focus on that they have a chance to really become one of the basketball powers in that conference because they are going to an elite conference. Right now, with what is happening with the Butlers and VCUs, anybody can elevate pretty quickly."
Hill, who was unavailable for comment Sunday, wanted to move fast and cast a wide net.
This was his second attempt to hire Krystkowiak -- he went after him after firing Giacoletti, but Krystkowiak took the Bucks job instead. Other names Hill reportedly considered include Saint Mary's coach Randy Bennett and former Alabama coach Mark Gottfried.
With Krystkowiak, the Utes get a coach with a background not that different from Boylen, who had experience in both college and the NBA. Among the players Krystkowiak coached with the Bucks was former Utah All-American Andrew Bogut.
Krystkowiak appeared in 71 games with the Jazz in 1992-93 and averaged just over seven points, but that one year under Jerry Sloan greatly influenced his coaching style.
"Jerry would never know it, but I loved his demeanor," Krystkowiak said in a Jazz website feature. "He doesn't wear anybody out with a lot of words, but when he opens his mouth, what he says is valid and you'd better be listening to what he is saying. I like his hard-driving style and having played under a number of different coaches, I enjoyed being underneath him."