The Blades were relegated from the Premier League on the final day of their first season back in the top flight after losing 2-1 to fellow strugglers Wigan on Sunday.
Warnock turned down a new contract at Bramall Lane recently, claiming the offer - worth around £750,000 had the club remained in the Premier League and £450,000 after relegation - was unacceptable.
After seven-and-a-half years at the club, the 58-year-old insisted he would renew talks with the club at the end of the season and it had been expected that he would remain with the Blades until their dramatic final-day defeat.
United plc chairman Kevin McCabe said: 'This is a mutual decision in some respects prompted by the events of the last couple of days.
'Both Neil and I believe it is for the good of the club.
'Neil departs with our best wishes.'
Warnock decided to go as he feared fans' opinion would have turned against him if he had stayed.
And he dismissed suggestions his departure had been prompted by a dispute over his new contract.
'I think they'll give a new man their backing but if I'd stayed that might be an issue,' said Warnock.
'Money has never entered into the conversation.'
He added: 'It's a sad occasion but I think it's one of tremendous satisfaction other than the disappointments over the last few weeks. A number of issues have left a bitter taste in my mouth.
'But when you look around where we were seven or eight years ago - we've got our own training complex, we've got a new breed of supporter.
'The pride has come back into Bramall Lane. We've done what we set out to do.
'The club is geared towards continued success. I definitely think we'll be the favourites of the three clubs going down to come back up.
'I think it's the right thing for both parties and some lucky man is going to take over a great set-up.'