Shurmur has a strong history of working with and developing quarterbacks. He succeeds Ben McAdoo, who was fired last month with four games remaining in a 3-13 season.
A source told ESPN's Adam Schefter that Shurmur received a five-year contract.
The former Cleveland Browns head coach became available after the Vikings were shellacked 38-7 in the NFC Championship Game on Sunday night in Philadelphia. Shurmur opted after the game to avoid talking much about his future, saying there was "another time and place for that."
"I want to thank [co-owners] John Mara and Steve Tisch for giving me the opportunity to be the head coach of the New York Giants," Shurmur said in a news release. "I am looking forward to getting to work with [general manager] Dave Gettleman and [assistant GM] Kevin Abrams and starting the process to once again build a championship team. I have been fortunate to work with many great coaches and players, and I am thankful for those relationships. I would like to thank my family and friends for their tremendous support."
"I can't wait to start working with Pat," Gettleman said in the release. "I know he will provide the type of leadership we need to take our team back to where it belongs. I have followed Pat's career for many years, and he has had great success wherever he has been. What struck me during our conversation is that being the head coach of the New York Giants is not too big for him. He is made for this moment and this opportunity."
Shurmur takes over a Giants team that has the No. 2 overall pick in this year's draft and could be in the market for a quarterback with Eli Manning turning 37 earlier this month. Early indications from the team and Gettleman are that the Giants will retain Manning for at least one more season, and he will have a chance to work with Shurmur.
The Giants chose Shurmur after interviewing six candidates. New England Patriots offensive coordinator Josh McDaniels and defensive coordinator Matt Patricia, Carolina Panthers defensive coordinator Steve Wilks, interim Giants coach and defensive coordinator Steve Spagnuolo and former Denver Broncos running backs coach Eric Studesville were also interviewed.
Shurmur, 52, was a longtime assistant with the Eagles under Andy Reid before becoming the offensive coordinator for the Rams under Spagnuolo. He then was the head coach of the Browns for two seasons, where he amassed a 9-23 mark. He later returned to Philadelphia as Chip Kelly's offensive coordinator before landing with the Vikings.
After the McAdoo era crashed in ugly fashion in its second season, the Giants were looking for a coach who had either been a head coach or had significant experience as a coordinator. Shurmur has both.
He is eyeing former Oakland Raiders coach Jack Del Rio to be his defensive coordinator, sources recently told ESPN's Chris Mortensen.
One source who worked with Shurmur called him a "really smart offensive coach" whose players love playing for him. His track record of success with quarterbacks in recent years is among his most impressive accomplishments. Shurmur has gotten career years out of Nick Foles, Sam Bradford and, most recently, Case Keenum.
The Vikings players raved about him as a coach and person.
"He's one of the best coaches I've ever played for," Vikings tight end Kyle Rudolph said. "He's a guy I had the pleasure of working with in the tight end room before he took over as offensive coordinator halfway through the year, and then working with him day in and day out this year, the way he's led the offense and took us -- even though we faced the adversity [of] losing another starting quarterback, another starting running back -- he carried us all the way to a top-10 offense.
"They are getting a really special coach, and as good a coach he is, he is an even better human being."
Keenum threw 22 touchdown passes and seven interceptions in 2017 while working with Shurmur. Minnesota finished 11th in total offense.
It helped him earn the opportunity for another head-coaching job. There is reason to believe it will turn out better the second time around.
"I think if he gets the opportunity, he'll be successful," Vikings coach Mike Zimmer said. "I was able to compete against Pat a few times when he was a head coach in Cleveland. I always thought his schemes did a good job. And then we brought him in here as one of the assistants.
"He's a smart guy, good relationship with the players. He's done an outstanding job this year and I do believe he's earned the right [to be a head coach]."
Shurmur inherits a difficult situation with the Giants. Their offense struggled badly for the second straight season, and three defensive players were suspended for their conduct. Shurmur will be tasked with trying to fix the offense and locker room.
"We are pleased to welcome Pat to our organization and look forward to the leadership he will provide for our team," Mara and Tisch said in the news release. "He has an outstanding track record in developing young players, and it is clear his players respond to his guidance and direction. We interviewed six talented and qualified candidates, and we feel like Pat, with his vision and experience, is the right person to lead our team."
Due to weather-related travel issues in and out of Minnesota, Shurmur's introductory news conference will be held on Friday. He will be at the Senior Bowl in Mobile, Alabama, from Tuesday until Thursday.