Marc Stein of The New York Times reported the news.
Kleber, 27, spent his first two NBA seasons in Dallas. He averaged 6.8 points, 4.6 rebounds and 1.1 blocks per game on 45.3 percent shooting.
While it's not a surprise that the Mavs are bringing Kleber back, the nearly $9 million average salary will open eyes. Kleber has flashed some ability to stretch the floor at the 4 spot but is a role player and a restricted free agent. The Mavs could have probably waited out Kleber's market and signed him at a lesser rate.
"It's cool, but at the same time, it's weird with a little bit of stress because you don't know what's going to happen," Kleber told Eddie Sefko of the Mavericks' official website last month.
"Obviously, you want to stay because I feel comfortable here and I love it in Dallas and I love the organization, the people, the team. I get along good with the coach. I like the system we play. But not knowing what's going to happen is weird. And the weirdest thing is you can't talk until July, so you just stay at home and wait."
Kleber also said he wanted to be part of the organization building around Luka Doncic and Kristaps Porzingis. It's likely Kleber will serve as Porzingis' primary backup.
The Mavericks also reportedly signed Seth Curry to a four-year contract Monday, so it appears they're emphasizing filling out their roster with shooting. With the exception of Dwight Powell, every player in the Mavericks' projected rotation for next season can stretch beyond the three-point line.
Dallas will in all likelihood attempt to add some bulk to its interior over the remainder of the free agency period, but don't be surprised if the Mavs lead the NBA in threes next season.