The arrival of Favre signals the end of Chad Pennington's career with the Jets. Tannenbaum said there would be another transaction regarding Pennington, who spent his first eight seasons with the Jets.
"It's a bittersweet moment for us," Tannenbaum said. "I have all the respect in the world for Chad as a person, as a player. We've accomplished a lot of good things with Chad. … He gave his heart and soul to this organization for a long, long time. I really appreciate everything he's done."
Favre left Green Bay on Wednesday, boarding a private plane that left for Hattiesburg, Miss., at 1:25 p.m. ET with his wife, Deanna, and 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."
Favre, who is 38, holds most major NFL passing records and led the Packers to the NFC Championship Game last season, where they lost to the New York Giants. Favre threw what would prove to be the decisive interception in overtime.
The Jets went into training camp with an open competition between Pennington and Kellen Clemens after neither established himself in 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.
Back in Green Bay, 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.
McCarthy told reporters 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 mindset 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."