Rapp is the No. 5 prospect at safety in the most recent rankings by ESPN's Mel Kiper.
Rapp announced his decision in a tweet less than 24 hours after the Huskies lost to Ohio State in a Rose Bowl game that he missed with a hip injury reportedly suffered in the Pac-12 championship game.
"Ever since I was a child, I dreamed of playing in the National Football League," Rapp wrote. "Now, with this incredible opportunity in front of me, I feel it is in my best interest to seize it."
Rapp finished the 2018 season with 59 tackles, five sacks, five pass breakups, three forced fumbles and two interceptions en route to earning first-team All-American honors from ESPN. Scouts Inc. projects Rapp, listed at 6-0, 200 pounds, as a second-round draft pick.
He came to Washington as a four-star recruit from Bellingham, Washington, and the fourth-ranked player in the state, choosing the Huskies over Notre Dame, Nebraska, Stanford, Colorado and others. He started 10 games as a freshman and turned into an All-Pac 12 selection as a sophomore.