The Mavs won the rights to Brand with a winning bid of $2.1 million, according to sources close to the process.
The league's 30 teams were notified shortly after 5 p.m. ET Friday that the Mavericks had lodged the winning waiver bid for Brand, who was released Wednesday by the Philadelphia 76ers through the amnesty clause in the NBA's new labor agreement.
"Excited," Brand said when reached Friday by ESPN.com. "I figured that I'd be claimed [off waivers] and that's definitely the destination I was hoping for."
The Sixers will still have to pay out the remaining balance of the $18.2 million owed Brand this season in the final year of his contract.
"It's going to be great playing with someone of Dirk Nowitzki's caliber," Brand said. "Chris Kaman is still a really good player and is going to show everybody that. And I've heard a lot of good things about Coach [Rick] Carlisle."
Only teams under the salary cap were eligible to bid on claiming Brand off waivers. He would have become an unrestricted free agent had he cleared waivers, but the Mavericks were determined not to let the opportunity to claim Brand pass as they continue their recovery from missing out on top free-agent targets Deron Williams and Steve Nash.
The Mavericks have rallied this week to add Brand, the former All-Star center Kaman and starter-level point guard Darren Collison all on one-year deals, enabling Dallas to preserve maximum salary-cap flexibility for the summer of 2013 and its planned pursuits of stars such as Dwight Howard and Chris Paul.
Dallas signed Kaman to a one-year deal worth $8 million on Wednesday and then completed a sign-and-trade deal Thursday with the Indiana Pacers to import Collison and swingman Dahntay Jones, with center Ian Mahinmi joining the Pacers.
Brand said he knows he'll be expected to play center alongside Nowitzki, despite the fact that the German is taller, but the former All-Star, now 33, said he welcomes the opportunity.
"I did it all last season," Brand said of guarding centers. "Of course, there's a few guys we all have trouble with, but I'm not worried about it all."