Rwandan prosecutors accuse Wenceslas Twagirayezu, 50, of inciting violence during the 1994 genocide.
He is alleged to have led a pro-Hutu militia in the north-west of the country that targeted ethnic Tutsis during the 100-day genocide.
He has lived in Denmark since 2001 and had been fighting against his extradition through the courts.
According to Rwanda’s pro-government New Times, Mr Twagirayezu is the second Rwandan to be extradited from Denmark . The first, Emmanuel Mbarushimana, was sentenced to life in prison in 2017, three years after his extradition.
Rwanda scrapped the death penalty in 2007 in an effort to encourage countries that oppose capital punishment to hand over genocide suspects.
It has issued international arrest warrants for more than 800 people it accuses of committing atrocities during 100 days of bloodshed in 1994.
An estimated 800,000 Tutsis and moderate Hutus were killed in the violence.
More on Rwanda’s genocide:
Rwanda: 100 days of slaughter
The real story behind Black Earth Rising
The photographs that reunited families
During the genocide, Mr Twagirayezu was a local official of the Coalition for the Defence of the Republic (CDR), a radical pro-Hutu party accused of inciting as well as carrying out violence.
A former primary school teacher, he led a local militia that operated in Rubavu District and which is suspected of planning the killing of civilians who had sought refuge at a university, the New Times reports.
Mr Twagirayezu, who has been in custody in Denmark since May 2017, is expected to arrive at the airport in the capital, Kigali, on Tuesday evening, the paper says.