The center, who was a first-round Draft pick in 2010, agreed a four-year contract extension with the team.
Speaking at a press conference, the 23-year-old said: "I'm blessed to be in this situation. I'm extremely happy. I'm glad we finally got this done. I usually have a lot to say, but I'm short on words today. I'm extremely happy.
"I like where this organisation is going, I believe in it, I'm glad they believe in me [and] I'm glad they gave me this chance to prove [myself] to them and this team.
"I'm big on loyalty. I've been like that my whole life. Since I started playing basketball, I was never really part of the big teams or the Hollywood teams. I was always the low-key guy and I just earned my way all the way through. I plan on doing the same thing here."
Cousins has averaged 16.3 points per game since coming into the NBA.