Club captain Holt, 31, looked destined for the Carrow Road exit when he tweeted that he had requested a transfer, but the striker appears to have mended his bridges with Norwich and could now see out his career there.
Holt, who scored 15 Premier League goals as Norwich easily avoided relegation last season, had tweeted: "Just to stop the rumour mill again. I have expressed to the board and the CEO that I want to leave the football club. Due to disagreements.
"I have loved my 3 years at the club and it sadness me to right this but want use to here it from me first. #lovedmytime"
However, he said on Tuesday: "I'm really pleased we've agreed things and that I've got a three-year deal which gives me and my family a bit of security.
"I do appreciate where the club was coming from in terms of the process we've gone through to get to this point. Now I'm just really keen to concentrate on getting back to work with the rest of the lads and concentrating on having a good pre-season and getting ready for the start of another season in the Premier League."
Norwich also confirmed the signings of Jacob Butterfield, on a four-year deal, and former Rangers man Steven Whittaker.
"It seems ridiculous that they're going to try and get him for as little as they possibly can," Hill told BBC Radio Sheffield. "The initial offer is an absolute joke. It's scandalous, disrespectful to Barnsley as well as the management teams and his team-mates.
"I'm disappointed with how the situation has lingered on and I would have liked business to have been concluded sooner than this."
Bradford-born Butterfield was made the club's youngest-ever captain last season at the age of 21 and a series of fine displays for the Tykes caught the attention of several top flight clubs before he sustained a season-ending knee injury against Leeds in December, which later required surgery to repair an anterior cruciate ligament.