Wilcox, 23, averaged 18.3 points, 3.7 rebounds, and 2.5 assists last season as a senior with the Huskies.
The 6-foot-5, 201-pound shooting guard was named Second-Team All-Pac-12 last season and is the school record-holder for most career 3-pointers.
He made a school-record 90 3-pointers last year and shot 39.2 percent from 3-point range, second in the Pac-12.
The Clippers shot 35.2 percent from beyond the arc last season, 22nd in the league.
Wilcox, a Pleasant Grove, Utah, native, also finished second in school history with 1,880 points. He shot 43.3 percent from the field and 84 percent from the free-throw line in his college career.
The Clippers also picked a shooting guard with their first-round pick last year, taking North Carolina's Reggie Bullock 25th overall.
It was Clippers' first draft under a revamped front office.
Head coach Doc Rivers assumed the role of president of basketball operations earlier this month, and general manager Dave Wohl, assistant general manager Gary Sacks and vice president of basketball operations Kevin Eastman have only been in their current roles since June 16.
Rivers orchestrated the front office restructuring with the team's ownership situation in limbo. Clippers owner Donald Sterling sued the NBA and is attempting to block the $2 billion sale of the team to former Microsoft executive Steve Ballmer.