Gettleman, who was sacked in July 2017, gave Stewart a one-year contract extension several months before he was relieved of his job.
Between the Panthers and Giants, this represents the second contract that general manager Dave Gettleman has given out to Stewart in his career.
The Giants will sign former Panthers running back Jonathan Stewart to a two-year deal, reports NFL Network's Ian Rapoport.
On Tuesday, Adam Schefter of ESPN first reported the expected signing, which can't become official until free agency opens Wednesday. Darkwa is an unrestricted free agent. "He's a terrific addition for us at this time". The team also has Wayne Gallman, who ran for 476 yards as a rookie last season, and third-year man Paul Perkins.
The Giants were 26th in rushing yards and tied for 28th in rushing touchdowns in 2017, so Stewart fills a need at running back to some extent.
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Stewart, who turns 31 this month, previously spent his whole career with the Panthers, drafted with the 13th overall selection of the 2008 draft out of Oregon. He did score six rushing touchdowns, but three of them came in a single game, against the Vikings in December.
Stewart rushed for a career-high 1,133 yards in 2009, when he teamed with DeAngelo Williams (1,117) to become the first set of teammates in National Football League history to each rush for more than 1,100 yards.
In 2017, Stewart played in 15 games with 10 starts.
Stewart worked with Shula extensively when the latter was moved from quarterbacks coach to offensive coordinator prior to the 2013 season.