The Blades turned down a reported £3.5million offer from Everton last month, but have now agreed to an undisclosed fee for the 20-year-old full-back, who is currently with the rest of Kevin Blackwell's first-team squad on a pre-season trip to Malta.
The club's international chairman Terry Robinson said: "We have accepted a bid for Kyle, that's correct. The two clubs have been negotiating this last week and we have agreed terms with Everton, but nothing has been agreed with the player.
"We won't be revealing the amount until any deal is done and our acceptance is conditional on Kyle reaching agreement with them over personal terms. It's a good deal for the player and Sheffield United. We wouldn't have agreed to it if it wasn't a good deal for the club."
Sheffield-born Naughton, 20, who has been at Bramall Lane since he was eight, burst on to the first-team scene at the start of last season and quickly established himself as a regular in Blackwell's side.
He soon attracted the attention of several top flight clubs and won his first England Under-21s call-up - against the Czech Republic in November - after just 11 Blades appearances.