The Royals have been searching for a new boss since they sacked Brian McDermott two weeks ago, and former Southampton manager Adkins has now taken the job on a contract until the summer of 2016.
Owner Anton Zingarevich said: “I am delighted to bring Nigel to our club because he is perfect for us.
"He has great respect within the game, his CV speaks for itself and he has many attributes as a manager, he is progressive, he develops players, his teams play attacking, passing football but most of all he knows how to win games at all levels.
"This is an appointment we have made both with the short and long term in mind and Nigel can take our club forward. I know our supporters have been keen to hear news over the past two weeks and I am certain they will join me in saying it was worth the wait. I wish Nigel and Andy nothing but good luck and now we focus on eight hugely important games in the Premier League.
"Our supporters will also play a vital part in the finale to the season and I am certain Nigel will get an excellent reception from our fans at the Emirates on Saturday."
The 48-year-old has been out of work since surprisingly losing his job with the Saints in January, with his sacking coming after back-to-back promotions.
Reading becomes his third professional club, having started out with Scunthorpe in 2006.
He stepped up to the manager's chair after serving the Iron as physiotherapist for 10 years and twice got them promoted from League One to the Championship.
A number of candidates had been linked with the post - Brighton's Gus Poyet was heavily touted last week - while Eamonn Dolan has been looking after the team on a caretaker basis.
The new manager inherits a side 19th in the Premier League and seven points shy of safety with eight games left.
Reading travel to Arsenal on Saturday before a home game against Southampton, Adkins's old side, on April 6.
Speaking for the first time since he left Southampton, he said: "I've not made any comments since I left Southampton and I want to take the opportunity to thank all the people there.
"I thank the fans, the players and supporters. We were on a fantastic journey but we have to move on now.
"I am pleased to be the Reading manager. We will take it one game at a time and try and keep this club in the Premier League.
"It's a good club, I've been impressed with them and I've always known what sort of club it is. We're in the Premier League and we want to stay there. I am excited."