Nate Dogg's Football Star Son -- HOLD UP ... I Committed to Washington

Nate Dogg's high school football star son Naijiel Hale is gonna be a Husky ... 'cause he officially accepted a full-scholarship to the University of Washington, TMZ Sports has learned.

Naijiel -- one of the top prep cornerbacks in the country -- tells us, "I'm very excited. I can't wait for this experience."

Hale tells us he's been working out in the gym twice a day and focusing on his speed -- while he currently runs the 40-yard dash in 4.6 seconds, Naijiel says he's working to bring it down to a 4.5 in the next 2 weeks.

As far as academics go, Hale says he's not sure what subject he wants to major in ... but tells us he's interested in studying music and business.