Contract terms weren't disclosed, but a source confirmed to ESPN.com's John Clayton that Ayers agreed to a two-year deal worth about $4 million.
The deal includes $1.75 million in guaranteed money and is loaded with incentives, according to the source.
Ayers' addition Wednesday makes him the 13th veteran player the team has signed since free agency started.
Ayers is the fourth participant from February's Super Bowl, and the third from the Broncos, to join the Giants. The others are cornerback Dominique Rodgers-Cromartie and return specialist Trindon Holliday. Cornerback Walter Thurmond left Seattle to join the Giants.
The Giants lost defensive captain Justin Tuck to Oakland in free agency, leaving Jason Pierre-Paul, Mathias Kiwanuka and second-year pro Damontre Moore up front. Pierre-Paul was limited by injuries last season.
Ayers never quite lived up to his draft status -- 18th overall in 2009 -- and had just 12 sacks in his five years with the Broncos, 5.5 of those coming last season.
He recorded 4.5 sacks in the first six games of the 2013 season, when Von Miller was suspended for violating the league's substance-abuse policy.
Ayers played outside linebacker when the Broncos ran a 3-4 defensive scheme under Josh McDaniels and defensive end in 4-3 alignments.
ESPN.com Broncos reporter Jeff Legwold and The Associated Press contributed to this report.