Aaron Wilson of the Houston Chronicle reported it's a two-year contract worth up to $16 million.
Rudolph had signed a four-year, $36 million deal with the team prior to the 2019-20 season, but he was the subject of speculation at the trade deadline last year as the Vikings grappled with more than $180 million worth of cap commitments over the next two seasons.
However, the Notre Dame product stayed and went on to end the year with 334 yards and one touchdown on 28 receptions in a season that came to a premature end due to a foot injury.
The 31-year-old was selected by Minnesota in the second round of the 2011 draft and recorded 4,488 yards and 48 touchdowns during his time with the team.
"[While] I understand that a lot of the news today is going to focus on me and the team parting ways, I'd personally rather focus on the flip side of that: the fact that me and the Vikings stayed together for 10 whole seasons...an insane run in today's NFL," Rudolph wrote in an article for The Players' Tribune.
Minnesota will now look to Irv Smith Jr., a second-round pick out of Alabama in 2019. In his second season, he posted 365 yards and five touchdowns on 30 receptions, a year after recording 311 yards and two touchdowns.
The Giants will likely use Rudolph in two tight end sets with Evan Engram, who made his first Pro Bowl in 2020.