Cousins' second 10-day contract expired Sunday. He signed his first 10-day contract with the team on April 5.
Cousins has averaged 8 points and 6.3 rebounds in 14 minutes in each of the team's past four games.
"This culture is one of a kind," Cousins said after Monday's 120-103 loss to theNew Orleans Pelicans. "Definitely one of the top organizations I have ever been a part of."
The 30-year-old veteran began the season with the Houston Rockets, who released him after 25 games in which he averaged 9.6 points and 7.6 rebounds.
The six-time All-Star has career averages of 20.6 points and 10.6 rebounds over 11 seasons.
ESPN's Ohm Youngmisuk contributed to this report.
Why Clippers made a great move signing Cousins for rest of season
Robert Horry and Richard Jefferson explain how DeMarcus Cousins benefits the Clippers after the team signed him for the rest of the season.
Cousins scores putback layup for first bucket with Clippers
DeMarcus Cousins puts back an offensive rebound for his first made basket on the Clippers.