The Packers had been talking with the Jets and Tampa Bay Buccaneers since deciding earlier this week that the team could no longer co-exist with one of the most beloved players in franchise history.
The Packers decided to move forward with Aaron Rodgers as their starter after Favre announced his retirement in March. Given their commitment to Rodgers, team officials weren't particularly receptive when Favre decided a little over a month ago that he might want to play after all - the latest development in several years' worth of flip-flopping about his football future.
"Brett has had a long and storied career in Green Bay, and the Packers owe him a tremendous debt of gratitude for everything he accomplished on the field and for the impact he made in the state," Green Bay officials said in a statement.
"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."
Jets chairman and CEO Woody Johnson issued a statement early Thursday.
"I am looking forward to seeing Brett Favre in a New York Jets uniform," Johnson said. "He represents a significant addition to this franchise, and reflects our commitment to putting the best possible product on the field. Mike Tannenbaum and his football administration staff did a great job of navigating this complex process. I am excited about welcoming Brett, Deanna and their family to the Jets organization."
The agreement was first reported by Fox Sports on its Web site.
Favre's new No. 4 Jets jersey already was for sale on the team's Web site about an hour after the trade was announced.
Favre left Green Bay on Wednesday, boarding a private plane that left for Hattiesburg, Miss. at 1:25 p.m. EDT with Deanna and agent James "Bus" Cook. Favre's family home is near Hattiesburg.
In Mississippi, Favre confirmed that he was considering the Jets and Buccaneers.
"We're working on it," Favre told Jackson TV station WJTV. "Hopefully, we can get something resolved. I've been saying that for quite a while now. I don't want to say we're running out of time, but I need to get into a camp somewhere."
The 38-year-old Favre holds most major NFL passing records and led the Packers to the NFC Championship last season, where they lost to the New York Giants. But Favre threw what would prove to be the decisive interception in overtime.
The Jets went into training camp with an open competition between Chad Pennington and Kellen Clemens after neither established themselves during a 4-12 season. Pennington was 1-7 as the starter and was benched midway through the season. Clemens went 3-5, but Pennington actually had the better season statistically.
With Favre's arrival, it's generally believed that one of the two will be traded or released - with the most likely candidate being Pennington.
After some hope for reconciliation between the franchise and perhaps its most beloved player earlier this week, the final split between the Packers and Favre became obvious Tuesday evening.
Packers coach Mike McCarthy told reporters on Tuesday that after approximately six hours of what he called "brutally honest" conversations over two days, the coach had determined that Favre doesn't have the right mind-set to play for the Packers.
McCarthy said Favre couldn't seem to get past emotional wounds that were opened as tensions mounted in recent weeks - even with the chance to win his starting job back potentially on the table.
"The train has left the station, whatever analogy you want," McCarthy said Tuesday. "He needs to jump on the train and let's go. Or, if we can't get past things that have happened, I have to keep the train moving."
McCarthy spoke to Favre again Tuesday night, but there was no indication that their conversation did anything to change the fractured relationship between Favre and the franchise.
"It was just very general," McCarthy said of the conversation with Favre, who was excused from practice Wednesday. "Just how he was doing, where he was with the process, things like that."
McCarthy said he was happy the rest of his players were getting a chance to move forward.
"We talked about it last night," McCarthy said. "The players want resolution, they want what everybody wants. To come out here every day and talk about somebody that is not here and then shows up, it's gone on too long, and understandably so. They want to play football."
Packers players vented frustration over the lingering Favre situation Tuesday, after fans chanting "Bring Back Brett!" turned practice into a zoo-like atmosphere and reporters continued asking questions about Favre instead of football.
After McCarthy made it clear that Favre's football future wouldn't be in Green Bay, players seemed to have some sense of closure.
Packers cornerback Charles Woodson - who said Tuesday that the saga had "gone on long enough" - said Wednesday that the Packers' front office gave players the answers they needed.
"From what I understand, for the most part it's taken care of," Woodson said. "Now it's just about the Packers and not about the situation. It's over now. From what I understand, it's pretty much over."