In Atlanta, Mack will reunite with Kyle Shanahan, the Falcons' offensive coordinator who held the same position with the Browns before leaving the team in 2015.
Mack is the second major departure for the Browns in free agency as wide receiver Travis Benjamin has agreed to a contract with the San Diego Chargers.
Mack voided the final three years and $24 million remaining on his contract on March 2, becoming a free agent. The 30-year-old center had to make a decision on the opt-out by March 4.
He was a first-round pick by Cleveland in 2009. A three-team Pro Bowl selection, he is considered one of the NFL's top interior linemen.
"We knew we needed to add an established presence along our offensive line," general manager Thomas Dimitroff said in a press release. "Alex is a three-time pro bowler and is an ideal scheme fit for our offense. We understand the importance of solidifying the center position and we have been able to do that today. We are pleased to be able to add Alex to our roster and believe he will be an anchor to our line."
Mack secured a five-year, $42 million contract, which included $18 million guaranteed, from the Browns in 2014 after the club used the transition tag on him. Jacksonville signed Mack to an offer sheet, which the Browns matched.
Later Wednesday, the Falcons announced that they had also agreed to terms with QB Matt Schaub. Schaub was picked by the Falcons in the third round of the 2004 draft and has also played for the Houston Texans, Oakland Raiders and Baltimore Ravens.
Also, wide receiver Mohamed Sanu is headed to Atlanta for a free-agent visit on Thursday.
ESPN's Pat McManamon contributed to this report.
Falcons fortify OL by signing Mack
Adam Schefter breaks down how former Browns center Alex Mack will contribute right away for the Falcons after signing a deal with Atlanta to become the highest paid center in the NFL.