On the women's side of the prestigious award, OR junior Sabrina Ionescu took home the prize after setting an NCAA record with 18 career triple-doubles.
The Duke University basketball star won the Jerry West Award, given each year to the top shooting guard in NCAA Division I men's basketball.
Earlier, Williamson won the Karl Malone power forward trophy.
Widely considered the top prospect for this year's draft, Williamson declined to say whether he would join Barrett and Reddish in declaring, drawing laughter from the crowd when he said, "Umm, who knows?"
"I think most of the country would say you graduated the oldest team in the country - there's no other team that had more experience in age than what Nevada had a year ago and now that's gone so the perception would be a dip", Alford said. "I enjoyed every moment of it".
Ionescu of OR was a surprise victor of the women's Wooden Award.
She also is the NCAA leader in triple-doubles and took home the Wade Trophy for the nation's most outstanding player this season.
Ionescu announced last Saturday that she would return for her senior season to contend for Oregon's first National Championship appearance. We played in the yard, and so this goes to them.
Gustafson had earned several post-seasonhonours, including AP player of the year for leading the nation in scoring for the second straight season.
Oklahoma Head Coach Lon Kruger will receive the 2019 John R. Wooden Legends of Coaching Award.
The individual awards were decided by a combination of fan votes and input from the Basketball Hall of Fame's selection committee.