The Norwegian joins the MLS side on a three-year contract from Valerenga in his home country,
pending the approval of a U.S. work permit.
Deila won two Ladbrokes Premiership titles and a Betfred Cup when he was manager at Parkhead between
2014 and 2016 and he is relishing the task ahead.
He told New York City's official website: "When the opportunity came up to join New York City FC as their new head coach, it was a dream come true for me to manage an amazing club in a great city.
"When I come in, it's important to continue to build on what's already proven to be a strong foundation and to get some of my ideas across.
"The way I want to play and the way NYCFC has played is very similar.
"I'm a very attacking coach. We want to have the ball as much as possible, but also try to be direct when you have those opportunities.
"I'm really looking forward to getting going and getting to know the players in pre-season and begin my time at NYCFC.
"I'm ready to see our supporters and hopefully we'll have a wonderful relationship.
"I'm going to do everything I can to play good football the City way and I'll give everything from myself to the club and I'm sure we're going to achieve fantastic things in the future."