Strahan, 36 -- a seven-time Pro Bowl choice -- reportedly will report to the team Monday, nine days before the Giants' regular season-opener against the Dallas Cowboys, and after 36 days after the start of training camp.
He was mulling retirement from his home in California.
New York Newsday also reported his return.
"He made up his mind last night," Strahan’s agent, Tony Agnone, told the newspaper. "I told him to sleep on it, make sure he feels right about it, and he woke up this morning and called (Giants General Manager Jerry Reese) and said he's coming back."
Strahan, the NFL’s single-season sack leader, missed most of the 2006 season because of a foot injury.
He faces a fine for his absence, the newspaper said.