Garn said in his letter of resignation, submitted Saturday to state House Speaker David Clark, "After discussing this matter with my family, I have decided that it is in the best interests of them, my colleagues and the people of Utah" to step down from the Legislature, the Salt Lake Tribune reported.
The report said Cheryl Maher, the teenager in the hot tub with Garn in 1985, said she felt "a lot of peace" since going public with her story.
Clark, like Garn a Republican, said he knew the resignation was coming but is still saddened.
"While there is no condoning of the events that took place, we certainly want to express our appreciation for the service Representative Garn demonstrated and our hearts and prayers are with his family," Clark said in an interview with the newspaper.
Garn admitted he and the teen had sat nude in a Salt Lake City hot tub, but insisted there was no sexual contact, the report said. However, Maher says there was touching and physical contact, though she doesn't give specifics.
When Garn ran for Congress in 2002 he arranged to pay Maher $150,000 in exchange for a promise not to disclose the incident, the newspaper said, even paying the money after losing the Republican primary.