The 22-year-old left the Etihad last summer and starred for the Dutch club as they finished second in the Eredivisie.
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City were able to trigger a buy-back clause in the Spaniard’s contract before announcing his return on Wednesday.
“I am thrilled to have rejoined City, a side playing incredible football under Pep Guardiola,” Angelino said.
“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 will provide competition at left-back for Benjamin Mendy and Oleksandr Zinchenko.
The Spain Under-21 international played every league game for PSV last season and a host of clubs were keen to sign him.
Wilfried Zaha always wanted to join Arsenal and has supported the club from a young age