The Premier League champions activated a 12m buy-back clause in the fullback's contract.
He has now signed a new four-year deal with City, who he joined from Deportivo La Coruna in 2012.
"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."