The deal was reported earlier Tuesday by the NFL Network.
The Giants also added a second Patriot to their team Tuesday, agreeing to a three-year, $10.5 million deal with linebacker Jonathan Casillas, a league source told ESPN NFL Insider Adam Caplan.
New York added the versatile Vereen as a change of pace to a backfield that already includes Rashad Jennings and Andre Williams.
Vereen was an unrestricted free agent for the first time this offseason after spending the past four years with the New England Patriots. He entered the market with his value at an all-time high, coming off a season in which he played in every game and totaled 11 receptions in New England's Super Bowl XLIX victory.
The 26-year-old played 52.9 percent of the Patriots' offensive snaps in 2014, which was the highest percentage among the team's backs. His ability to run precise routes, reliability catching the football and willingness and effectiveness picking up the blitz made him a vital cog in New England's offense.
The 5-foot-10, 205-pound Vereen totaled 99 receptions over the past two seasons. In 2014, he rushed for 391 yards on 96 carries with two touchdowns.
A second-round draft pick in 2011, Vereen is known more for his elusiveness than ability to create after contact, as evidenced by his 1.23-yard average after contact in 2014, which ranked 69th out of 73 running backs with at least 50 carries, according to ESPN's Stats & Information.
ESPN.com Patriots reporter Mike Reiss contributed to this report.
Shane Vereen To Sign With Giants
Dan Graziano breaks down why the Giants decided to sign RB Shane Vereen.