Set to earn Palmeiras £32m upfront with a further £2.2m available in add-ons, the 22-year-old has put pen to paper on a five-year contract, stepping in for compatriot Savio following his own £75m switch to Tottenham last week.
Manchester City's new winger built his reputation at Palmeiras' academy, going on to register nine goals and a dozen assists across 96 first-team outings for the Brazilian club.
"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," Elias 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. I want to be the best footballer I can be and the conversations I've had with the people at City so far has convinced me there isn't a better place for me to fulfil my ambitions."
The move continues an extraordinarily active window for Enzo Maresca's squad, with City having now spent more than £230m this summer following the earlier arrivals of Elliot Anderson from Nottingham Forest for £116m and Ayyoub Bouaddi from Lille for £85.6m.
The club remain in talks with Liverpool over Cody Gakpo and are keen on Chelsea's Enzo Fernández, even as they have already recouped more than £286m in sales - Rodri to Barcelona for £65m, Tijjani Reijnders to Al-Qadsiah for £52m, and further significant fees for Nico González and James Trafford, while Omar Marmoush's loan to Tottenham includes an obligation to make the move permanent next summer for £60m.
Elsewhere, Swansea are closing in on a separate loan deal for City's 17-year-old winger Monga, who is due to travel for a medical ahead of Tuesday's deadline, with Finland international Leo Walta set to leave the Welsh club on loan for Los Angeles in a related departure.
Monga came through Leicester City's academy, where he became the youngest goalscorer in Championship history as a 15-year-old, before signing a five-year contract at City this summer following 30 appearances for the Foxes last season.
City director of football Hugo Viana had previously described Monga as "an exciting player" who has "already made huge strides in his young career," and the move to Swansea, who are also closing in on Huddersfield's Tom Iorpenda, offers him a pathway to regular senior football in the Championship.