Green announced he was leaving Kentucky last week, and the Huskies immediately emerged as the early favorite. Washington coach Mike Hopkins recruited Green while Hopkins was at Syracuse, which finished second to the Wildcats for Green out of high school.
Green visited the Huskies' campus earlier this week.
Green, a 6-foot point guard from Philadelphia, averaged 8.0 points and 2.3 assists this season for Kentucky, shooting 42.3 percent from 3-point range. As a freshman, he averaged 9.3 points and 2.7 assists but was playing a significantly bigger role for the Wildcats.
He was ESPN's fifth-ranked point guard and No. 24 prospect overall coming out of high school in 2017.
Green will be eligible to play in January 2020 and will have a year and a half left to play for the Huskies.
With starting point guard David Crisp graduating after this season, Green should slot into the starting lineup immediately for Washington.