Andrei Kirilenko is returning to the NBA, this time with Minnesota.

The Timberwolves found the versatile, tough-defending small forward they’ve been seeking to fill out their roster, and this one they didn’t have to try to pry away from a division rival.

Kirilenko’s signing of a two-year, $20 million contract was completed Friday after a three-team trade with New Orleans and Phoenix cleared the necessary space under the salary cap. The 31-year-old Kirilenko spent last season with CKSA Moscow after a 10-year run with Utah, choosing to play in his native Russia during the lockout and staying there once it ended.

“I think playing a more regular schedule in Europe helped his body. He told me he feels tremendous. He feels as good as he’s ever felt,” Timberwolves president of basketball operations and general manager David Kahn said. “I think that, if anything, it was probably a small advantage for him to not play in the NBA.”

Kirilenko, currently playing with the Russian national team at the Summer Olympics in London, won the Most Valuable Player and Best Defender awards in the Euroleague. In a statement provided by the team, he said he’s excited to be coming back to the United States, where he has dual citizenship.

“The Wolves have one of the best coaches in the league in Rick Adelman, and I feel my game fits in well with his style of play,” Kirilenko said. “I also like the talent that Minnesota has on the team with star players like Kevin Love and Ricky Rubio.”

All 10 of Kirilenko’s NBA seasons have been with the Jazz, who selected him with the 24th overall pick in the 1999 draft. He averaged 12.4 points, 5.6 rebounds and 30.8 minutes per game during that time, including an All-Star 2003-04 season when he averaged 16.5 points, 8.1 rebounds, 2.8 blocks and 1.9 steals. He has 62 games of five or more blocks and 14 games of five or more steals.

The Timberwolves signed restricted free agent Nicolas Batum to an offer sheet and also tried to swing a sign-and-trade deal with Portland, but the Blazers didn’t budge and kept the 23-year-old from France. So the Wolves turned to Kirilenko, a 6-foot-9 budding superstar at one point whose productivity waned over the last few years under the weight of a variety of injuries.

“We see somebody who can help us in a number of ways,” Kahn said, “and frankly is the kind of player we didn’t have on our team.”

With all of the dominant, score-from-anywhere-on-the-floor wing players in the league these days, the Wolves need to keep them in check.

“By no means am I suggesting that Andrei can shut them down, but I at least think now we can send somebody out there with the wingspan and the capabilities of guarding them a little bit,” Kahn said.

That could’ve been translated as a slight against Derrick Williams, who plays the same position as Kirilenko, had an up-and-down rookie year and has found himself the subject of trade talks.

“Derrick should be challenged to seize what he wants, as opposed to it simply being handed to him,” Kahn said. “There will be no limitations on Derrick’s ability to play here from a minutes standpoint, but it’ll be up to him to determine.”

The rebuilding project is clearly over for the Timberwolves, with the addition of another veteran. They’ve now sent away two first-round draft picks, one on paper (Kahn said it’s protected for the next few years if it falls in the top 13) and one in person (Wes Johnson was the fourth overall choice in 2010 but struggled mightily over two seasons here) to the Suns. They received three future second-round picks in the Suns-Hornets trade.

They plan to sign guard Brandon Roy and center Greg Stiemsma next week, leaving Kevin Love, Nikola Pekovic and Luke Ridnour as the only players who’ve been on this roster more than one season.

Whatever becomes of these latest transactions by the wheel-and-deal Wolves, at least their best player is in a better mood.

Love spoke at a meeting with the media in London on Friday, where Team USA was preparing to begin Olympic play. The All-Star power forward said he’s feeling better about the shape of the roster after seeing the moves Kahn has made this month. Recently, Love publicly urged the organization to add veteran players to the young core, expressing impatience with becoming a playoff team.

With Kirilenko, Roy, Stiemsma, Shved and Cunningham coming, Love sounded more confident in the plan.

“I’m happy with it,” Love said. “I know a few weeks ago I didn’t necessarily sound that way. But I just want to make the playoffs.”

Love noted that he’s the only member of Team USA whose NBA career doesn’t include postseason experience.

“I’m thirsty for that. I’m hungry for that. I think postseason play is the next thing for me. I’ll be headed into my fifth year, so it’s definitely due,” he said.

Kahn, on the conference call, was asked if Love approved of the moves.

“I read the assistant general manager’s comments just a moment ago,” Kahn said, poking a little at Love’s previous lobbying. “I’m very pleased that he’s pleased.”