New Falcons owner Arthur Blank is expected to pursue Tampa Bay personnel director Tim Ruskell. Blank and Wolf negotiated over the past weekend before Blank offered Wolf a contract on Monday.
Wolf, 63, averaged $2.3 million over the last three years of his contract with the Packers. He is being paid $500,000 a year as a consultant by the Packers.
"Everything I have I owe to professional football," Wolf told the Milwaukee Journal Sentinel. "I had to make a total commitment to Arthur Blank and the Atlanta Falcons. I was very honored to have that opportunity.
"But the bottom line is that I can't make that commitment. One needs a total commitment to do that job and I couldn't do it."
The offer, believed to be a record for a general manager, was worth $9 million over two years if he and Blank mutually decided to end the relationship at that point, and $13 million if Wolf departed after three years, according to ESPN.com.
Wolf retired as general manager of the Packers on June 1. He built the Packers into perennial NFL contenders during his nine-year tenure, highlighted by Green Bay's Super Bowl XXXI win over the New England Patriots after the 1996 season.
Wolf currently splits time between homes in Annapolis, Md., and Jupiter, Fla.
The Packers were seeking a high draft pick from the Falcons as a form of compensation for luring Wolf out of retirement. It never was determined what selection the Packers would have received.