In the deal, Dampier will receive a seven-year, $73 million contract, ESPN The Magazine's Ric Bucher has learned.
Dallas sends Christian Laettner, Eduardo Najera, two future first-round draft picks and the draft rights to guards Luis Flores
and Mladen Sekularac to the Warriors for Dampier, Dan Dickau, Evan Eschmeyer and the draft rights to Steve Logan.
The 6-foot-11 Dampier averaged career highs of 12.3 points and 12 rebounds in 74 games last season for the Warriors. He was fourth in the NBA in rebounding, and one of just nine players to average more than 10 points and 10 rebounds a game.
Dampier opted out of his contract with the Warriors in late June and became a free agent after seven seasons with Golden State.
Donnie Nelson, the Mavericks president of basketball operations, was in Greece for the Olympics and not immediately available for comment.
A call to Dampier's cell phone was not immediately returned Tuesday evening.
While Dampier gives the Mavericks a much-needed big man for coach Don Nelson, Golden State achieved some objectives as well with the trade.
"We acquired quality players who can help our team now and several prospects that bode well for our future," said Chris Mullin, the Warriors' new executive vice president of basketball operations.
Najera averaged 4.9 points and 3.9 rebounds a game in his four seasons with the Mavericks, shooting 51 percent from the field. He was limited by knee problems last season.
Laettner, a 12-year veteran, spent the last three seasons in Washington before being traded back to Dallas on draft night. He has averaged 13.3 points and 6.9 rebounds over 819 career games
with Minnesota, Atlanta, Detroit, Dallas and Washington.
Flores was the 55th overall pick by Houston in the June draft, but acquired by Dallas. Sekularac, who has played professionally in Europe since 1996, was the 55th overall pick by Dallas in the 2002 draft.
Dickau was traded from Portland to Golden State last month, and Eschmeyer missed all of last season due to multiple knee operations after going from Dallas to the Warriors in another multiplayer trade last summer. Logan was a second-round pick by the Warriors two years ago.
Information from The Associated Press was used in this report.