He was found guilty of crimes against humanity for sending his troops to rape, beat up and loot from the population of Fizi on New Year’s Day.
Forty-nine women came to testify in the court in in Baraka.
The BBC’s Thomas Hubert says it is the first conviction of a commanding officer for rape in eastern DR Congo.
Humanitarian agencies regularly cite government troops as the largest single group of perpetrators of widespread sexual violence in the Kivu region, says our reporter, who is in the town of Baraka, not far from Fizi.
Our reporter says some of the estimated 2,000 people who attended the verdict proceedings, reacted angrily to the sentences.
This woman is one of the 49 rape victims who gave evidence
“The people are not happy with this judgement; the people were expecting the death sentence,” one man in the crowd told the BBC.
Lt Col Mutware is one of many former rebels who joined the army as part of peace agreements in 2009.
The judges said the state should pay compensation to the more than 60 women were raped on 1 January in Fizi.
Our reporter says it is unusual for such large numbers of victims in eastern DR Congo to be willing to testify against their rapists.
Ahead of the verdict, many of them gathered at the rape victims’ centre in Fizi.
“I was fleeing the violence but unfortunately I met four soldiers,” a 29-year-old mother of five told the BBC about the events on New Year’s day.
“They began to tear the pants I was wearing. They took my child from my arms and left him on the ground. Then they had sex with me.”
In August 2010, rebel forces were accused of raping hundreds of women, girls, men and boys around the town of Luvungi.
The UN recorded some 11,000 rapes in 2010 – the true figure is believed to be much higher.
Our reporter says since January there have been other reports of sexual violence in an area where the Rwandan FDLR rebels are still active, 40km (about 25 miles) from Fizi.
Medical charity Medecins Sans Frontieres says it is planning to deploy a mobile clinic to the area on Monday after receiving credible reports of 30 new rapes last week.
It says it has treated more than 70 victims of rapes in two similar incidents in the area between 19 January and 4 February.