The Spain international will become permanent on a five-and-a-half-year deal at the end of the season.
He leaves the Portuguese giants only one year after joining permanently from Manchester City, winning the Primeira Liga title in 2021.
The North Londoners were believed to have been closing in on a deal to sign the 23-year-old defender over the weekend, but a move did not materialise after Sporting reneged on the terms.
Porro has scored 12 goals and registered 20 assists from 98 appearances for Sporting in all tournaments.
— Pedro Porro (@Pedroporro29_) January 31, 2023