The running back left the Giants at the end of the NFL season, but had been a free agent since being waived by the San Francisco 49ers in December.
The 31-year-old told the team's website: "Whatever they need me to do, whatever role they want me to play, I'll come in and do it. I know the offense. I know they've made some tweaks here and there, and I'll do whatever I have to do.
"The Giants have given me a great opportunity. This is where I wanted to be. These are the coaches I want to play for and I wanted to come back with my teammates. This is the place I love most.
"I'm ready to go. If I need to go Sunday, I can go Sunday. There's no issue. I'll be really excited."