Porro, 19, is reported to have cost City £11million (€12m) from Girona and is expected to be sent back on loan to a club in LaLiga.
The versatile right-sided player broke into Girona's team last season, playing 32 times in LaLiga as the Catalan club was relegated to the second tier.
But Porro was a standout performer despite Girona's woes, showing great potential in several roles, occupying the full-back, wing-back and wide midfield positions on the right flank over the course of the campaign.
Borussia Dortmund and Schalke were among the clubs linked with him, but City pipped the competition to secure Porro's signature.
Carson, 33, has also joined City on a season-long loan from Championship side Derby County, providing back-up to Ederson and Claudio Bravo after youngster Aro Muric joined Nottingham Forest on a temporary deal.
"It's an honour to have signed for City on loan," Carson told the club's website. "It's something I didn't expect but an opportunity I simply could not turn down. To be part of this squad – the champions of England – is a dream come true.
"I can't wait to see Pep's work on the training field up close. What he has achieved in his management career has been amazing, and it's every player's dream to play under him."