McAdoo, who has served as the offensive coordinator under Coughlin for the past two seasons, will be introduced at a news conference on Friday morning. He never has been a head coach.
"I am honored," McAdoo said in a statement. "... I have been very fortunate to have a lot of great coaches, administrators and players take an interest in me and my career. It has been a privilege to work and learn under Coach Coughlin.
"I have been preparing for this moment my entire professional life, and without the guidance and support of many people, I would not be here right now."
McAdoo has earned praise for his work with quarterback Eli Manning, who has thrown 65 touchdowns and 28 interceptions and completed 62.8 percent of his passes the past two seasons.
"Ben is an outstanding young coach who has great experience and has done a good job as our offensive coordinator these past two years," team president John Mara said in a statement. "Jerry [Reese, the team's general manager] and I interviewed six impressive candidates, and when we were through with that process, we had another conversation with Ben, as did Steve and Jon Tisch.
"We were all impressed with his energy, his enthusiasm, his vision and his desire. Ben has been preparing for this opportunity since he started coaching, and he has earned his stripes every step of the way. Some have suggested he may not be ready, and as I said last week, we want a coach who feels like he has something to prove."
Steve Spagnuolo will be retained as the team's defensive coordinator, a league source told ESPN's Ed Werder on Wednesday.
Former Miami Dolphins head coach Joe Philbin is among the favorites to join McAdoo's staff as offensive coordinator, sources told ESPN. McAdoo and Philbin worked together on theGreen Bay Packersunder Mike McCarthy.
"I'm excited," Manning said in a statement. "I'm excited for the Giants organization and for the team. I think Coach McAdoo is a great coach, a great teacher, and will be a great leader of this team. I'm excited to continue to work with him and grow within this offense, and get this organization back where it needs to be."
McAdoo, 38, will be the NFL's second-youngest coach. Adam Gase, the Chicago Bears offensive coordinator who was hired by the Dolphins, is 37.
Reese and McAdoo said they're looking foward to working with each other.
"Ben is very excited, and I'm very excited and happy for him," Reese said. "... Can't wait to get moving with the offseason."
Said McAdoo:"We have a lot of work to do, and it will take a collaborative effort for Jerry and I to achieve what is always the goal for this franchise: another Lombardi trophy."
McAdoo also interviewed last week with the Philadelphia Eagles for their head-coaching job, and their interest might have helped him strike a deal with the Giants, who think very highly of him and probably didn't want to risk losing a potential coaching star to a division rival.
The Giants have been seeking a replacement for Coughlin, who resigned last week after coaching the team to two Super Bowl championships in his 12 seasons in New York.
McAdoo joined the NFL in 2004 as an offensive quality control assistant with the New Orleans Saints, spent the following year with theSan Francisco 49ersand then joined the Packers, where he stayed for the next eight seasons, working with the tight ends and spending his the final two years there as Aaron Rodgers' quarterbacks coach.
The Giants hired him in 2014 to replace Kevin Gilbride, and his version of the West Coast offense -- and the addition of Odell Beckham Jr.-- has helped revive the offense.
The Giants had the NFL's eighth-best offense in terms of total yards and ranked sixth in the league in total points this past season.
The Associated Press contributed to this report.
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