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 the New 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.