Shula, who will coach the Giants' quarterbacks as well, was fired from the Carolina Panthers last month.
The 52-year-old Shula spent five years as the offensive coordinator of the Panthers, with new Giants general manager Dave Gettleman serving in the same role with Carolina for the first four of them before being dismissed in July.
Shurmur will call the plays while Shula will play a primary role in devising game plans, the Giants announced.
"I've known Mike a very long time," Shurmur said in a statement. "He's done an outstanding job developing and working with quarterbacks. He was the offensive coordinator of a team that was recently playing in the Super Bowl. They've done an excellent job on offense in Carolina. We share a vision in terms of what we want to do offensively. We're excited that he'll be with us.
"He'll be the offensive coordinator and also work with the quarterbacks. He'll assume all the roles that any offensive coordinator would have, and he'd obviously be in position to call it, if need be."
Giants quarterback Eli Manning endured a difficult season in which he saw his 210-game consecutive start streak halted. New York, which finished with a 3-13 mark, scored just 15.4 points per game -- second only to the winless Cleveland Browns (14.6).
Under Shula's watch, Carolina's offense failed to find its rhythm this past season after leading the league in scoring in 2015. The Panthers finished 19th in total offense (323.7 yards per game) and 28th in passing (192.3) during the past regular season.
Shula spent seven seasons total with the Panthers, working his first two in 2011-12 as the team's quarterbacks coach.
Also on Thursday, the Giants added Tyke Tolbert, Hal Hunter and Ben Wilkerson to the offensive staff. Tolbert will serve as the team's wide receivers coach, Hunter as offensive line coach and Wilkerson as assistant offensive line coach.
"(With) Hunter, there's a little bit of a scheme fit," Shurmur said of the 35-year coaching veteran. "He's done a good job coaching the offensive line wherever he's been."
The Giants also added Gary Emanuel as defensive line coach, Lou Anarumo as defensive backs coach and Deshea Townsend as assistant defensive backs coach.
Special teams coordinator Thomas McGaughey and assistant Anthony Blevins are also new to the Giants.
"I knew Thomas in the profession, and after having a chance to visit with him, I knew it would be a perfect fit here," Shurmur said. "He's an outstanding coach. He coached top-10 units in special teams."