The Islanders also acquired Minnesota's 70th pick in the deal, which was earlier reported by Newsday.
Islanders general manager Garth Snow said Clutterbuck provides the team with "immediate help."
"We got a good young player that's established in the NHL and we love the element of grit," he said. "Obviously he's had success at putting the puck in the net and creating offense."
Clutterbuck, who chipped in with four goals and six assists this year, has also been a perennial leader in the hits category, though his new teammate Matt Martin earned that honor this season with 234.
The 20-year-old Niederreiter was a highly-regarded prospect after being selected fifth overall in the 2010 draft, though his relationship with the organization soured in the past year.
Niederreiter was not invited to training camp with the team before the 2013 season began, which prompted his agent to ask Snow for a trade.
Asked if there was a rift between the two camps, Snow said: "I'm not gonna speak from their perspective, but for us, no."
The Islanders finally moved Niederreiter, adding some snarl and edge to their lineup with Clutterbuck.
Clutterbuck, a 25-year-old restricted free agent, was a former teammate of Islanders star center John Tavares in the Ontario Hockey League.
Snow indicated that the prices were high on the draft-day floor for an NHL-ready player.
"I gave up a former first-round pick, so yeah, you gotta give up something to get something," Snow said.
Wild general manager Chuck Fletcher said his club was interested in Niederreiter three years ago, but he was off the board well before Minnesota could grab him. Fletcher wasn't concerned at all about how Niederreiter would fit in now following a change of scenery.
"We have done a lot of homework on him over the years. We did a ton of homework on him leading up to the 2010 draft," Fletcher said. "There were no red flags from our perspective. At the end of the day, he is a 20-year-old player, and like every 20-year-old kid, maybe he made a couple of decisions that five, 10 years later you look back and say, 'Why did I do that?' -- like the rest of us.
"He will certainly have a clean slate with us. His size and scoring ability are two ingredients that we can certainly use."
During his brief news conference, Snow sidestepped questions about his goaltending situation, particularly regarding the status of beleaguered goaltender Rick DiPietro, whose 15-year, $67.5 million deal does not expire until 2021.
DiPietro remains a prime candidate for a compliance buyout, though the Islanders have given no indication of whether they intend to use it to part ways with the former first overall pick.
"Well, we don't have to make that determination today," Snow said. "We're focused on the draft. We'll make any decision at the appropriate time and now is not that time."
Asked if the oft-injured DiPietro has been medically cleared -- a team cannot buy out an injured player -- Snow declined to answer.
"I'm not going to get into end-of-year physicals with every player, whether he was with the Islanders or Bridegeport," he said. "I have to get back to the draft."
DiPietro was waived during the lockout-shortened season and spent most of the schedule with the team's AHL affiliate, the Bridgeport Sound Tigers.
The Islanders don't have a clear-cut option in net for next season, with starter (and UFA-to-be) Evgeni Nabokov expected to test the market on July 5 and back-up Kevin Poulin still in need of some seasoning.
Information from The Associated Press was used in this report.