The Lakers announced the deal Monday, one week before training camp opens.
Ellington is a five-year NBA veteran who has played for Minnesota, Memphis, Cleveland and Dallas. He is averaging 6.4 points, 1.8 rebounds and 1.0 assists over 312 career games.
The North Carolina product averaged career-bests in shooting percentage (.437) and 3-point percentage (.424) for the Mavericks last year, appearing in the playoffs for the first time.
Los Angeles has 14 players under contract for training camp. The Lakers missed the playoffs last season for just the third time in 38 years, finishing with their worst winning percentage in more than a half-century.