A Wisconsin man has pleaded guilty to kidnapping 13-year-old Jayme Closs and killing her parents.

His admission spares the girl, who was held captive in a remote cabin for three months, from having to testify at his trial.

Jake Patterson, 21, sniffled as he pleaded guilty to two counts of intentional homicide and one count of kidnapping on Wednesday. As part of a plea deal, prosecutors dropped a count of armed burglary. Patterson faces up to life in prison when he is sentenced on 24 May. Wisconsin does not have the death penalty.

Jayme Closs escaped after 88 days held captive in Patterson’s cabin. Photograph: Fbi Handout/EPA

Patterson had said he would plead guilty in a letter sent this month to a Minneapolis TV station, saying he did not want the Closs family “to worry about a trial”.

Patterson admitted kidnapping Jayme after killing her parents, James and Denise Closs, on 15 October at the family’s home near Barron, about 90 miles (145km) north-east of Minneapolis. Jayme escaped in January, after 88 days in Patterson’s cabin near the small, isolated town of Gordon, 60 miles from her home.

The plea, coupled with an earlier decision by prosecutors not to bring charges in the county where Jayme was held, increases the chances that the details of her time in captivity will remain private.

Patterson answered “yes” and “yeah” to repeated questions from the Barron county judge James Babler about whether he had understood what he was doing. Later, as he responded “guilty” to each count, he could be heard sniffling. He paused for several seconds after the judge asked him about the kidnapping charge before stuttering “guilty”.

The defence attorney, Richard Jones, told the judge that Patterson “wanted to enter a plea from the day we met him” and brushed off strategies presented to him, including trying to suppress his statements to investigators.

Members of the Closs family and Patterson’s father and sister all left court without commenting.

According to a criminal complaint, Patterson told the authorities he decided Jayme “was the girl he was going to take” after he saw her getting on a school bus near her home.

During Jayme’s time in captivity, Patterson forced her to hide under a bed when he had friends over and penned her in with tote boxes and weights, warning that if she moved “bad things could happen to her”. He also turned up the radio so visitors couldn’t hear her.

Authorities searched for Jayme for months and collected more than 3,500 tips. On 10 January, Jayme escaped from the cabin while Patterson was away. She then flagged down a woman who was out walking a dog and pleaded for help. Patterson was arrested minutes later.