In a corresponding move, the Giants promoted former Cleveland Browns wide receiver Corey Coleman to the active roster, according to NFL Network's Ian Rapoport, who first reported Harrison's trade on Wednesday.
Dealing Harrison would represent New York's second big trade in as many days after it sent cornerback Eli Apple—a 2016 first-round pick—to the New Orleans Saints for a 2019 fourth-rounder and 2020 seventh-rounder.
Harrison was in the midst of his third season with the Giants and had spent the first four years of his career with the New York Jets.
The 29-year-old veteran has made 31 tackles, including four for a loss, through seven games in 2018.
Giants safety Landon Collins posted a series of tweets in reaction to Harrison's departure:
The G-Men signed Harrison to a five-year, $46.25 million deal in 2016, and he has two seasons remaining on the contract beyond 2018.
Harrison was named a first-team All-Pro in 2016 when he racked up 86 tackles and 2.5 sacks as part of a dominant Giants defense. New York dropped off considerably as a team last season, but Harrison was still productive with 76 tackles, 1.5 sacks and a career-high-tying seven tackles for loss.
In Detroit, Harrison is set to fill the run-stuffing void left by the offseason departure of Haloti Ngata.
He will join a defensive tackle rotation that includes Sylvester Williams, Ricky Jean Francois and 2016 second-round pick A'Shawn Robinson.
The move to Detroit will give Harrison a far better chance of competing in the playoffs this season since the Lions are 1.5 games behind the Minnesota Vikings in the NFC North at 3-3. They are also just a half-game out of a wild-card spot.
Meanwhile, the Giants are tied for the NFL's worst record at 1-6.
Harrison figures to provide a major boost to a Detroit defense that ranks just 30th in the NFL against the run.