From Russia with . . . nothing shady.

That was the finding of a “thorough” NBA investigation into the Nets’ summer signing of free-agent forward Andrei Kirilenko, multiple league sources told The Post. The league, after getting complaints from at least one other team that suggested improper agreements, examined the signing and found nothing against the rules.

Kirilenko, who made roughly $10 million in Minnesota last season, opted out of the final year of his Timberwolves’ deal and took the Nets’ $3.1 mini mid-level exception.

In doing so, he triggered a wave of anger and suspicion. Rival owners and execs intimated under-the-table deals existed between Kirilenko and fellow Russian Mikhail Prokhorov, the Nets billionaire owner.

At least one owner — possibly more — complained to the league.

“When there is a formal complaint, the league will look into it,” said one league official who spoke in generalities and refused comment on the Kirilenko issue.

So the league launched its investigation, questioning participants. Nets officials were summoned — at one point over a weekend, which is usually a time off in the summer for league execs.

“It was a very, VERY, thorough investigation,” one source maintained. “They checked everything.”

Marc Fleisher, Kirilenko’s agent, addressed only Kirilenko’s decision to join the Nets. He declined to acknowledge whether the investigation occurred.

“Basically, the offers and things we had from other teams were too difficult to make happen,” Fleisher said, referring to the necessity of a possible sign-and-trade or complicated deal.

And in the end, the chance to play with a legitimate contender, even for considerably less, was the final tipping point.

Prokhorov addressed the matter in July when the Nets introduced trade acquisitions Kevin Garnett, Paul Pierce and Jason Terry. Kirilenko was vacationing and not available for the press gathering, which Prokhorov flew from Russia to attend.

“Old stereotypes, they’re very hard to beat and to break,” Prokhorov said of the suspicious eye cast upon a Russian dealing with a Russian. “I respect all the NBA rules and we play by the NBA rules. But I want just to stress once again like with luxury tax, I will do whatever I can in order to win championship but under the NBA rules. Please make no mistake about this.”

Prokhorov’s barbs at Knicks owner James Dolan — including referring to him as “that little man” in a New York Magazine article and the placing of the massive 22-story “Blueprint for Greatness” billboard featuring the Nets owner and Jay Z near the Garden — prompted the Knicks head to complain to the league.

As a result, as The Post reported exclusively, NBA Commissioner David Stern brokered a “cordial” meeting over lunch for the two owners to avoid a full-blown Hatfields and McCoys re-creation, multiple sources said.