The 24-year-old centre-back Dias was also named England’s Footballer of the Year in the annual vote of the Football Writers’ Association last month following a superb debut campaign after his move from Benfica last year.
Dias, who played a key role in delivering City’s third Premier League title in four years as well as the League Cup, also helped them reach the Champions League final.
He is the fourth defender to be voted Player of the Season by the public, the captains of the 20 Premier League clubs, and a panel of experts after Manchester United’s Nemanja Vidic, former City captain Vincent Kompany and Liverpool’s Virgil van Dijk.
Dias’ compatriot Cristiano Ronaldo won the Premier League Player of the Season award for United in 2006-07 and 2007-08.