The Wizards also announced Friday they waived forward Okaro White.
Baker has averaged 3.3 points and 1.8 assists in 92 career games, all with New York. The Knicks released him Dec. 13.
Wizards president Ernie Grunfeld calls Baker a "tough and physical defender who can give us added depth in the backcourt."
Baker was an undrafted rookie in 2016 out of Wichita State, where he averaged 13.2 points for his career. He helped the Shockers upset No. 1 Gonzaga in the 2013 NCAA tournament.