A Packers' Web site report said terms of the trade were not immediately available.
"It is with some sadness that we make this announcement, but also with the desire for certainty that will allow us to move the team and organization forward in the most positive way possible," team CEO and President Mark Murphy said.
"We respect Brett's decision that he could no longer remain here as a Packer. But there were certain things we were not willing to do because they were not in the best interest of the team."
Favre announced his retirement in March but later changed his mind. NFL commissioner Roger Goodell reinstated Favre Sunday and he was added to the Packers' roster but did not practice with the team.
"We appreciate the tremendous passion shown by our fans," Murphy said. "We, like them, always will see Brett Favre as a Green Bay Packer and our respect for him never will change."
Favre set many major passing records during his 16 years at Green Bay, including most touchdowns (442).