Law enforcement officials said the suspect, Robert Eugene Koehler, a 60-year-old registered sex offender, was arrested Saturday at his home in Palm Bay, Fla., about a one-hour drive from Orlando. He was charged with two counts of sexual battery with a deadly weapon stemming from a rape that the authorities say he committed on Dec. 28, 1983, when a 25-year-old woman was stabbed with a sharp object and raped in her home in Miami-Dade County.

Katherine Fernandez Rundle, the Miami-Dade state attorney, said at a news conference on Thursday that a DNA sample taken from Mr. Koehler had linked him to 24 other sexual assaults from that era.

The key break in the case came last year, Ms. Rundle said, when Mr. Koehler’s son was arrested on a felony domestic violence charge, requiring him to submit a DNA sample to a criminal database. That sample, she said, provided a close familial match with samples collected from the rapist in the 1980s.

“This familial contact was the breaking point for us,” she said. “It was just what we needed to be able to piece this all together.”

Laura Adams, a county prosecutor, said that when the police searched Mr. Koehler’s home, they found several safes stashed with women’s jewelry and a metal nail file wrapped in a protective covering. She said investigators believe Mr. Koehler may have kept the items as souvenirs from his crimes.