Dias' move sees Nicolas Otamendi move in the opposite direction, while the fee surpasses the £62.8m paid to Atletico Madrid for defensive midfielder Rodri last season.
The 23-year-old will take the No 3 shirt at the Etihad after being tracked for more than two years by City, who are said to be confident that they have found the right player to partner Aymeric Laporte.
“To have the opportunity to join a club like Manchester City is a fantastic opportunity for me and one I couldn’t turn down," Dias said.
“Their success speaks for itself. They have been the dominant team in England over the last few years, playing an attacking brand of football which I feel suits my own game.
“It is really exciting to be part of such a talented squad and to play for a world class manager like Pep Guardiola, who has a proven track record of developing young players like myself.
“I believe I can improve here, at a club whose ambitions match my own and I will give everything to be successful and win titles.”
City are convinced that Dias' age, profile and ability will make him a successful signing, and the replacement for Vincent Kompany that they have long needed.
“Ruben is a player we have admired for some time and we have been impressed with how he has progressed at Benfica," said Txiki Begiristain, City's director of football.
“He has developed into a real leader and as a defender, he has all the attributes we are looking for. He is strong in the air, good in one v one situations and technically, he is very good, so we are confident he can thrive in our system.
“He is young but has gained valuable experience at a big European club in Benfica and we’re really pleased we’ve been able to sign him. He is another talented addition to the squad and someone who is only going to get better working under Pep.”