Eugene Nkuranyabahizi, 41, was arrested in Norway in May last year but has lived in the country since 1999.
Rwanda, which formally asked for his extradition in August, wants him to stand trial over allegations that he took part in the 1994 genocide, in which 800,000 people were killed.
The former teacher is accused of having participated in massacres in the areas of Nkakwa and Cyahinda, where some 7,500 people died in April 1994.
The suspect, who has Burundian citizenship, denies all the charges and opposes his extradition.
The district court of Stavanger in southwest Norway ruled that despite "several different explanations and observations" the allegations in the extradition request were based on "reasonable grounds".
The court also judged that the suspect's rights would be respected in Rwanda and that he would be treated fairly by the country's legal system.
One of Nkuranyabahizi's lawyers said his client intended to appeal the ruling.
"We disagree both with the legal considerations and the evaluation of evidence that was examined," Brynjar Meling told Norwegian media. "The court certainly noted a number of deficiencies and inconsistencies in the testimonies, but did not draw the right conclusions," he said.
The extradition announcement comes as Rwanda holds a series of commemoration ceremonies to remember those who died, with thousands crowding into the national stadium in Kigali for a memorial service on Tuesday.
Last year Norway extradited Charles Bandora to Rwanda to stand trial for his alleged role in the genocide.
A court in Oslo also gave the highest possible prison sentence — 21 years — to another Rwandan, Sadi Bugingo, after he was found guilty of taking part in the slaughter of more than a thousand Tutsis in his home country.