The defender will join Nick Cushing’s side on 1 July on a two-year deal and will wear the number 35 shirt.
Fidalgo is a Portuguese Champion, having helped former club SC Braga to win their first league title in the 2018/19 season, and becomes Cushing’s second signing of the summer, following in England international Ellen White’s footsteps.
The 25-year-old hopes to achieve more success with the reigning FA Cup and Continental Cup winners.
"It feels like a dream come true," she told CityTV. "I was overwhelmed when I heard it was going to be a reality.
"I'm really happy to be here. The league is super competitive and that's something I was looking for.
"The team is huge. Everyone knows how big Manchester City is and I'm really happy to be here."
Fidalgo was born in Lisbon and started her professional career at CF Benfica in 2009, where she played 63 times, scoring 10 goals.
The 25-year-old won one national title in the 2015/2016 season and was nominated Best Player by the Sindicato dos Jogadores Profissionais de Futebol.
The right-back also captained her team, before she signed for rivals Sporting CP in 2017. Fidalgo played there for one season, scoring one goal for the Lions, before moving to the north of Portugal, to wear SC Braga’s colours.
On the international front, the Portugal star has represented her country in several international competitions, playing 43 times for the senior national team, since her debut in February 2011.
She hopes that joining City will lead to more regular international appearances, in addition to more silverware for Cushing's side.
Describing her playing style and personality, Fidalgo believes she is an ideal fit for City both on and off the pitch.
"I'm very feisty," she smiled. "I'm always trying to do better and I always give my best, even when things are not going well.
"The thing that I think describes me best is my attitude. I really go for it until the game has ended - I don't stop fighting.
"I want to win and I know how good it is to win. Sometimes, you learn more when you don't win but of course, winning is great and it's what I intend to do here."
Interestingly, Fidalgo, who lived in Brazil, is Bernardo Silva’s distant cousin from their great-grandparents’ side.
Our new signing also has a Master’s Degree in Environmental and Energy Engineering. She deems the Brazilian Ronaldo as her favourite player.
Reflecting on his latest signing, manager Cushing declared: "Matilde came on our radar about a year ago we’ve been tracking her performances for a while now.
"She’s a committed defender with a strong desire to win every game she is playing in and that winning mentality will be key next season when we’re competing on all four fronts.
"We’re delighted to have her at Manchester City and excited to help take her game to the next level.”