The 22-year-old has signed a four-year contract which keeps him at the Etihad Stadium until the summer of 2023, and he cannot wait to get started with the Blues.
"I am thrilled to have re-joined City, a side playing incredible football under Pep Guardiola," said Angelino.
"Watching them while playing in Holland has been a pleasure. City's performances over the last two seasons have been incredible and I am very excited about returning and contributing to the club's bid for more success.
"I believe my own game can develop under Pep's management and I am very confident that the club will go from strength to strength over the next few years."
Angelino came through the City Academy but made just three senior appearances in his first period with the club.
He has previously had loan spells at Girona, Mallorca and NAC Breda.
City Director of Football Txiki Begiristain added: "Angelino is a hugely talented young player and is an accomplished defender with great potential.
"Over the past year, he has gained excellent experience playing in the Eredivisie and the Champions League with PSV Eindhoven.
"We're sure that he will bring additional defensive quality to our squad."