Following the sacking of Chris Hughton in April, Adams took temporary charge at Norwich with the club five points above the drop zone.
However, four defeats and one draw in Norwich’s remaining five Premier League games led to their relegation.
But despite demotion to the Championship, the club insist Adams “achieved a notable improvement in performance and attitude from the players”.
A club statement also said: “Throughout the process his passion for the club, his commitment to playing attractive, winning football, his hunger to succeed and his desire to continue to progress young, talented players through to the first team squad shone through.”
Norwich chief executive David McNally has also promised to back Adams in the transfer market this summer.
“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,” he said.
“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.”
Adams has pledged that “attractive and winning football” will be “the norm” at Carrow Road next season.
“It is a huge honour and I am immensely proud to be confirmed as the club's manager going forward, and work starts straight away on putting into place the necessary requirements for next season,” said the 48-year-old.
“The priority is to ensure that attacking, attractive and winning football is once again the norm for supporters of this club, and it is essential that we now have everyone pulling in the same direction for the challenges that lie ahead.
“I thank the Board of Directors for giving me this opportunity as well as the amazing support that I and the team received from the fans during the last five games of last season and also in the time since, and I can assure everyone that we will all be working as hard as possible to achieve our objective of returning this club back to where it belongs.”