Alves completed his move to Paris Saint-Germain today on a free transfer after leaving Juventus after just one season.
The Brazil international was widely expected to reunite with his former Barcelona manager Guardiola at Manchester City.
Guardiola is desperate to recruit full-backs after releasing Pablo Zabaleta, Bacary Sagna and Gael Clichy this summer.
But the 34-year-old, who has three Champions League titles to his name, snubbed City and hopes to use his experience to guide PSG to a European title.
During his official unveiling to the media, the Brazilian said: "If Pep Guardiola and Manchester City feel hurt, I am sorry.
"I have come here to be a champion. I've had the pleasure of winning the Champions League three times and I want to bring my experience here."
City is said to have failed in their pursuit of Alves after PSG hijacked their move with the last minute offer.
The mega-rich Ligue 1 side are said to have doubled City's offer of a £115,000-a-week contract to lure Alves to the French capital.
City is now expected to re-double their efforts to sign Tottenham and England right-back Kyle Walker.
Guardiola has spent big already this summer, with midfielder Bernardo Silva joining for £43million and goalkeeper Ederson arriving in a £35m deal.
Source: Daily Express