The source, who did not wish to be identified because a contract hasn't been signed yet, said Monday that the deal is "verbally done."
Gooden said on his Twitter page Monday that he had three deciding factors in his decision to join the Mavs: winning, playing time and money. He wrote: "Dallas is the team!"
Owner Mark Cuban did not return an e-mail seeking confirmation of the deal, but did post "Welcome Drew" on his Twitter page.
Gooden, 27, played in 19 games for the San Antonio Spurs last year, averaging 9.8 points and 4.4 rebounds. The 6-foot-10 Gooden averages 12 points and 7.9 rebounds and will help a frontcourt that lost Brandon Bass to free agency.
The Mavs would be his seventh team.