NFL Network insider Jason La Canfora first reported the deal, which a league source said is a two-year contract.
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Responding to initial reports of a deal, Finley tweeted, "It's TRUE! Thank you so much to the Packers organization, all of my fans, and my beautiful wife. Happy Bday. Let's GO Packers!! Back soon..."
"I could not be happier to have the privilege of being a Packer for the next 2 yrs. Glad to be back with my team & coaches for 1 common goal," he also tweeted.
The Milwaukee Journal Sentinel reported that Finley will receive $5.75 million in 2012 and $8.25 million in 2013.
Finley, who was scheduled to become a free agent, and the team had been in negotiations for some time. By reaching the deal, the Packers avoided having to use the franchise tag to keep Finley.
A league source told the Journal Sentinel that the deal was meant to be a compromise, giving Finley more than he would have received had the Packers franchised him as a tight end ($5 million per year) and less than he would have made as a wide receiver ($9 million).
Finley had 55 receptions for 767 yards and scored eight touchdowns this past season.
Wells, a center, also is scheduled to become a free agent next month.