Kevin Blackwell's side needed to win to stop the Blades going up on Saturday and were on course when Rob Hulse scored two minutes after the break.
Five minutes from time, substitute Stephen Hunt bundled home an equaliser from a Ivar Ingimarsson header.
Leeds manager Kevin Blackwell:
"I want to congratulate them on a fantastic achievement, Neil Warnock and the boys deserve credit.
"To get promoted over the course of the season is no mean achievement but we've pushed them all the way.
"Many people thought that it was a two-horse race at Christmas but we pulled them in and really worked hard to try to rein them in."
Reading assistant manager Wally Downes:
"The target after we lost to Luton was to go through the rest of the season unbeaten.
"It would have been easy to lose it after Luton, but to their credit the players are unbeaten since then.
"We don't want to lose until the end of the season. If we get the record great, but the target is to be unbeaten."
Leeds: Sullivan, Kelly, Butler, Kilgallon, Crainey, Miller, Bakke (Moore 83), Derry, Douglas, Healy (Beckford 86), Hulse (Graham 76).
Subs Not Used: Bennett, Pugh.
Goals: Hulse 47.
Reading: Hahnemann, Murty (Gunnarsson 83), Sonko, Ingimarsson, Shorey, Oster (Hunt 64), Harper, Sidwell, Convey, Doyle (Long 78), Kitson.
Subs Not Used: Stack, Makin.
Goals: Hunt 85.
Att: 24,535
Ref: M Halsey (Lancashire).