Nottingham Forest's failure to beat Cardiff sent the Magpies back up to the top flight at the first attempt ahead of their home clash with Sheffield United, which they went on to win 2-1.
Hughton said: "This is a wonderful achievement and we are absolutely delighted. That we have secured promotion with six games to spare is testament to this set of players and how good a season they have had."
Billy Davies' Forest side went into the match 15 points behind the Magpies with five games remaining but can no longer catch their rivals following a 0-0 draw at the City Ground.
Peterborough's one-year stay in the second tier is over after a 2-2 draw at Barnsley yesterday. Posh knew that only a win would keep their season alive.