The club's return to the English top flight was confirmed on Saturday when QPR and Derby County both suffered away defeats.
Leicester had beaten Sheffield Wednesday the previous day and can now look forward to playing in the Premier League for the first time since 2004.
"It feels fantastic," Morgan told the Leicester Mercury.
"We did our job on Friday night and we still have six games to go so we just want to concentrate on becoming champions now.
"It is definitely the greatest achievement of my career so far to achieve promotion. It is amazing and something I haven't done before.
"To captain Leicester and do it is even more special."
Manchester United report: Antony's future has already been decided after new comments from CEO
‘Slot hasn’t come in and changed everything, making it all about himself – it’s been about the players he’s inherited, getting the best out of a system he likes’: Liverpool manager impressing former players with personality and tactical approach
