"Allan is a really exciting player, and we think he will be a big addition to the squad," City's Director of Football Hugo Viana said in a statement on Monday. "He has shown throughout his short career so far that he will fight to be the best he can be."
According to reports, City have agreed to pay around €40 million ($47 million) for the player who came through the academy ranks at the Sao Paulo club and made 96 first-team appearances.
Elliot Anderson, Geronimo Rulli, Ayyoub Bouaddi, Jeremy Monga and Pierce Charles have also joined the club during this transfer window.
"This is a surreal moment for me. Manchester City, with everything they have won over the past 15 years, are one of the most attractive clubs in the world for players," Allan said.
"To be able to sit here today and say I have joined them is the proudest moment of my life. I love Palmeiras and always will -- but the decision to come to City was an easy one."
Florianopolis-born Elias said he hoped to be "another good Brazilian" in the Premier League and follow in the footsteps of the likes of Gabriel Jesus, Ederson and Fernandinho, who all won Premier League titles with City.
