The imam, 54, was shot in the head in the stairwell of his home in Stromsund.
He was initially in a coma and is now suffering from brain damage.
The imam's family have accused the Uzbek government of orchestrating the crime, but the court ruled that it was clear that Yury Zhukovsky "acted on behalf of someone in Russia".
The court said that the evidence presented was not sufficient for it to say with certainty whether the Uzbek state was involved.
The February 2012 attack on the imam, Obid-kori Nazarov, sent shockwaves through Stromsund, a small town of just a few thousand inhabitants in sparsely populated northern Sweden.
The town is home to hundreds of Uzbek asylum seekers who have fled the repressive government in their home country, thousands of miles away.
Many are devout Muslims who fell foul of the authorities for practising their religion outside of government control.
Mr Nazarov fled Uzbekistan in 1998 after an arrest warrant for extremism was issued against him. He went into hiding in neighbouring Kazakhstan until the UN approved his refugee status eight years later, allowing him to go to Sweden in 2006. He has always denied being an extremist.
Judge Goran Ingebrand said on Tuesday that "everything indicated" that there was a connection between Zhukovsky and "someone in Russia".
He said the defendant had made and received at least 34 telephone calls and text messages to a number in Russia on the day Mr Nazarov was shot.
Zhukovsky was extradited to Sweden in August from Moscow where he had been detained under an international arrest warrant. He admitted tracking down Nazarov's location in Sweden but has denied carrying out the shooting.
The imam's son on Tuesday accused the Uzbek government of being behind the assassination attempt.
Human rights organisations have accused Uzbekistan of imprisoning thousands of Muslims whom it depicts as extremists seeking to overthrow the government and set up an Islamic state.
Mr Nazarov had a reputation for criticising his country's record in dealing with social and economic problems and human rights. Correspondents say that as such he was a prime target of the Uzbek security services.
In July 2012 a court in Sweden cleared a man and woman from Uzbekistan of aiding the assassination plot against Mr Nazarov, which correspondents have described as reminiscent of a Cold War undercover operation.
The court ordered Zhukovsky to be deported after serving his time. His lawyers say he may appeal against his conviction.
A Swedish court has sentenced an Uzbek man to 18 years in prison for the 2012 attempted murder of a Muslim cleric who criticised the Uzbek government.