Westbrook, a guard, was taken fourth overall out of UCLA. White, a forward, was drafted by Detroit with the 29th overall pick out of Indiana and traded to the Sonics for the 32nd pick (Walter Sharpe) and the 46th selection (Trent Plaisted).
Westbrook and White signed on Friday, Seattle general manager Sam Presti said. Contract terms were not released.
The NBA's rookie scale calls for Westbrook to make about $6 million during his first two seasons, while White would make about $1.6 million combined in the first two years.
The SuperSonics announced this week that they will be moving to Oklahoma City starting next season.
Westbrook averaged 12.7 points and 4.3 assists last season as a sophomore at UCLA, where he was also named the Pac-10 defensive player of the year.
White averaged 17.4 points and 10.3 rebounds as a senior at Indiana last season, earning Big Ten player of the year honors.