Valanciunas, who had one year left on his contract after being traded to New Orleans this offseason, is now tied to the franchise for three years and $44.1 million.
Valanciunas said he took the preseason to get a feel for the franchise and ultimately decided he wanted to be a part of the team's long-term vision.
"It was good for me so I decided I wanted to stay here," Valanciunas told reporters Wednesday. "If they wanted to keep me, I would be really happy to stay here. I felt like this was my family here. I'm happy now.
"From a coaching standpoint, they understand me and what I do. We have good teammates. They've welcomed me. The organization has been great and helping me out. They made it feel like I've been here for a long time so I wanted to come back."
He's also coming off his most productive season after averaging 17.1 points and 12.5 rebounds while shooting a career-best 59.2% overall in just 28.3 minutes a game.
Valanciunas finished third in the league in rebounding last season and second in offensive rebounds per game (4.1) -- two spots ahead of Adams. He also was tied for third in the league in double-doubles (49) just behind Nikola Jokic and Russell Westbrook.
With the extension out of the way, Valanciunas said now he can focus on the upcoming season, which starts Wednesday night against the Philadelphia 76ers.
"Now we have a lot of stuff to do," Valanciunas said. "We have to prove that we can be really good, prove that we can learn how to win the games. We are able to do that. We have the talent. The coaching staff is really good for us. Now we have to put in that work and win some games now."