David McNally's Twitter account said he had left following his club's defeat against Manchester United. The tweet was later deleted and the club did not comment.
Norwich City Football Club confirmed on Monday that McNally had resigned.
"Everyone at Carrow Road wishes him all the very best for the future," it said.
McNally resignation: 'Norwich City top brass under increasing scrutiny'
The statement on the club's website said: "The board of directors had unanimously agreed to accept McNally's resignation and would like to place on record their sincere gratitude for David's game-changing contribution to the football club since he joined in the summer of 2009.
"David played a leading role as the club erased crippling debts and rose from the lower reaches of League One to the Barclays Premier League.
"Director of finance Steve Stone has been appointed interim chief executive and the board and everybody at the club is totally focused on supporting Alex and the players, as we head in to Wednesday night's vital Premier League game against Watford at Carrow Road."
On Saturday, McNally replied to a fan on Twitter who called on him to leave the club after the defeat by Manchester United.
The fan blamed a lack of investment for the Canaries current plight - facing relegation from the lucrative Premier League.
In a tweet, he said: "I understand your view. I've resigned tonight and I hope the club can now progress."
David McNally's departure is a hugely significant moment for Norwich City. This was the man who ran the club on a day-to-day basis and had the final say on most things, from player transfers to what was on sale in the club shop.
He arrived in 2009 with the club at its lowest point in 50 years following relegation to League One.
He oversaw successive promotions, four of the past five seasons in the Premier League and the club clearing all external debt - all of which will count in his favour in the eyes of Norwich City supporters.
But with the prospect of a second relegation from the top flight in three seasons looming, the club's top brass was coming under increasing scrutiny.
Then, hours later, Mr McNally seemingly retracted his resignation, insisting he remains fully committed to the club.
The tweet said: "I take back what was said earlier. I remain fully committed to NCFC and to Delia and Michael and I've not resigned. My apologies."
Both tweets were then deleted.
The Canaries' current predicament sees the club four points from safety with two games to play. On Wednesday, they face Watford at home and then Everton away on the last day of the season.
Both Newcastle United and Norwich City will be relegated to the Championship if Sunderland win on Wednesday.
A strong ally of co-owner Delia Smith, Mr McNally arrived at Carrow Road in 2009 from Fulham having previously spent four years as sales and marketing director at Celtic.
Norwich City fans on Twitter have praised McNally and thanked him for his work at the club, while others have questioned the timing of his departure.
MrTomParsley said: "The loss of @davidmcnally62  just made the inevitable relegation a lot more worrying, he deserves only respect & thanks from all #ncfc fans."
Dan Brigham of the Little Yellow Bird Project, which produces podcasts on Norwich City, told BBC Radio Norfolk: "I interviewed him earlier this year and he said he wanted to leave a legacy, leave Norwich City with a 35,000-capacity stadium, and a first class training facility.
"He will see this [Norwich City facing relegation] as a real failure, as not part of the plan.
"We're not relegated yet, so the timing is weird."
Norwich City chief executive David McNally has quit the club following a tweet on Saturday in which he seemingly announced his resignation.