Dias has moved to City in a deal worth £65m.
“Ruben is a player we have admired for some time and we have been impressed with how he has progressed at Benfica," said Begiristain.
"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."
Dias has signed a six-year deal, the longest initial contract handed to a City player - although Ederson was handed seven years, Aymeric Laporte six and a half and Bernardo Silva six, all as extensions to their first deals.