NFL Network insider Jason La Canfora first reported the deal, which a league source said is a two-year contract.
"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.
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.
Other Packers players took to Twitter after the news broke Wednesday.
Wells, a center, also is scheduled to become a free agent next month.