Hamilton's second 10-day contract with the Clippers expired Tuesday, and the Clippers need the extra man power while Jamal Crawford remains sidelined with a right calf bruise.
Hamilton averaged four points, 1.4 rebounds and 0.3 assist per game in 9.6 minutes a game over eight games, including two starts for the Clippers.
The shooting guard/small forward sustained a sprained right ankle in a game against the Houston Rockets on Sunday, but Clippers Coach Doc Rivers said the team would "most likey" extend his contract anyway.
Hamilton was drafted as the 26th overall pick by the Dallas Mavericks in 2011. He was then traded to the Denver Nuggets on Draft Day. Hamilton has career averages of 5.7 points and 2.7 rebounds in 13.1 minutes a game over 134 games with the Nuggets, Rockets and Clippers.
Tweeted Hamilton: "Happy to finally be a @LAClippers! Nothing like putting on a jersey every night for your #HomeTownTeam!"