The Wizards waived veteran guard Gary Neal, who is expected to miss at least three more weeks with quad and hip ailments, to create a roster spot to sign Thornton.
"Marcus brings experience and shooting to our backcourt and helps us fill a void caused by Gary's injury with another veteran player," Wizards president Ernie Grunfeld said in a statement. "His skill set will allow him to fit right in to our system and give our offense another option."
Thornton negotiated a buyout with the Houston Rockets before the March 1 deadline to ensure that he would be playoff-eligible for his next team.
The Miami Heat also had strong interest in Thornton but couldn't sign him for luxury-tax reasons after point guard Beno Udrih, whose contract the Heat bought out in February, went unclaimed on waivers.
Thornton joins trade-deadline acquisition Markieff Morris and recent signee J.J. Hickson as high-profile newcomers for the Wizards, who awoke Wednesday in 10th place in the Eastern Conference at 30-33, 2½ games out of a playoff spot.
Guard Bradley Beal did not travel on the Wizards' three-game road trip this week because of a sprained pelvis.