The pick is lottery-protected in 2023, top-12 protected in 2024, top-10 protected in 2025, top-eight protected in 2026, or becomes two second-rounders after that point, The Athletic's Shams Charania reports.
"Having the opportunity to acquire a player of Russell's caliber and character was something that we could not pass up when looking at both the immediate and long-term future of our team," Wizards general manager Tommy Sheppard said in a statement.
He added: "With that said, the decision to part ways with John, one of the greatest players in franchise history, was extremely difficult. What he has meant to our organization and our community is immeasurable and will not be forgotten."
Both guards reportedly requested trades this offseason.
Sheppard and Rockets executive Rafael Stone reached an agreement within a few hours on Wednesday afternoon after the two sides hadn't spoken on a potential deal for weeks, ESPN's Adrian Wojnarowski reports.
The Wizards GM previously said he had "no plans" to deal Wall, though owner Ted Leonsis reportedly had the final say.
"At the end of the day, this is a Ted (Leonsis) call," a source told The Athletic's David Aldridge.
Wall is set to earn $41.3 million this season and $44.3 million the following year. He holds a $47.4-million player option for the 2022-23 campaign.
He hasn't appeared in an NBA contest since December 2018. Wall is the Wizards' all-time leader in assists and steals.
Meanwhile, Westbrook is owed $41.4 million this coming campaign and $44.2 million in 2021-22. He also holds a $47.1-million player option for the 2022-23 season.
His move to the nation's capital reunites him with former Oklahoma City Thunder head coach Scott Brooks.
"Russell's accomplishments and honors on the court speak for themselves, but his drive and will to win are what separate him as a truly unique player," Brooks said in a statement.
Westbrook averaged 27.2 points, 7.9 boards, and seven assists during his lone season in Houston.