He was voted by his City team-mates as the Players' Player and won an online poll by the fans for the Players Player.
It capped an excellent season for club captain Morgan, who was also named in the PFA Championship Team of the Year on Sunday night.
Frenchman Anthony Knockaert also picked up two awards. He was named the Young Player of the Year, and his sublime goal at Huddersfield, when he back-heeled Paul Konchesky's cross over his own head to score City's second goal, was voted the goal of the season.
City's 3-2 home win against Bolton was voted by manager Nigel Pearson and his staff as the performance of the season, while goalkeeper Kasper Schmeichel was recognised with the Champagne Moment for his game-changing save in the 3-0 win against Blackburn in February.
Midfielder Michael Cain's promising displays for the club's Under-18s and table-topping Under-21 side gave him the edge in a close race for the Academy Player of the Year honour, with forwards Harry Panayiotou and Joe Dodoo also in the running.