Adams was handed the reins on a caretaker basis in April following Chris Hughton's sacking, but was unable to keep the Norfolk club in the Premier League.
The likes of Malky Mackay, Gianfranco Zola and Neil Lennon were linked with the Carrow Road hotseat, but Norwich confirmed on Thursday that Adams has been charged with the task of getting them back into the top flight.
Adams, a former Norwich midfielder, has been handed a three-year contract and chief executive David McNally is in no doubt he is the right man for the job.
McNally told the club's official website: "Neil impressed us when he stepped up to the plate for the last five games of the season in the most trying of circumstances and he's continued to impress us during a very rigorous round of talks about the full-time managerial position.
"He is a very talented coach who is hungry to succeed at Norwich City, playing the kind of football we want to see.
"The club is in a strong position off the pitch, with no external debt and capacity crowds expected at Carrow Road yet again next season.
"We have the nucleus of an excellent squad and Neil will be given funds to refresh and strengthen the squad where required.
"It's now time for everyone connected with the club to give their full support to Neil as we focus on the future of this great club and prepare for the vital weeks and months ahead."
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