George played his first seven seasons for the Los Angeles Lakers before signing with the Mavericks in 2006.
An agreement was first reported by ESPN.com's Marc Stein last week.
Citing George's agent Mark Bartelstein, ESPN.com reported that the deal is for two years and approximately $4 million.
George earned NBA championship rings in each of his first three seasons with the Lakers and blocked a deal earlier this year to be traded to the Nets in exchange for point guard Jason Kidd and other players.
The Mavericks ended up trading point guard Devin Harris, center DeSagana Diop, swingman Maurice Ager, forward Trenton Hassell and retired forward Keith Van Horn to New Jersey along with two first-round draft picks and $3 million.
Kidd, who earned a gold medal at the 2008 Beijing Olympics, averaged 9.9 points and 9.5 assists in 29 games for the Mavericks after the trade.
George averaged 3.7 points and 2.6 rebounds a game for the Mavericks last season.
The 6-foot-8 forward has averaged 5.8 points and 3.3 rebounds a game during his NBA career.
"Getting Devean back in a Mavs uniform has been a goal of ours all summer," Mavericks coach Rick Carlisle said in a statement. "His experience and ability to run the floor and play and defend multiple positions will be a great asset for us this season."
Information from The Associated Press was used in this report.