Alves was unveiled as the club’s second signing of the close season on Wednesday after joining PSG in a two-year deal on a free transfer following his exit from Juventus last month.
The 34-year-old won three Champions Leagues and six La Liga titles at Barcelona, whose former manager Pep Guardiola had hoped to lure Alves to Manchester City.
But the right-back turned down the chance to reunite with Guardiola as PSG offered Alves a deal worth 14 million euros ($16 million, £12.4 million) a year, according to reports in France, twice what City had been willing to pay.
“I didn’t only have interest from Manchester City but other clubs in England as well,” said Alves.
“I have friends here, my wife likes the city and that’s why I changed my mind.
“If Guardiola feels wronged, I apologise for that. If Manchester City feel annoyed, I am sorry as well but I take responsibility.”
Alves passed a medical in the French capital before he was presented at a press conference in Paris, holding aloft his new shirt with the number 32 on its back.
He quit Italian giants Juventus two weeks ago after helping them to a Serie A and Coppa Italia double while also reaching the Champions League final in his only season in Turin.
“Our goal is to win the Champions League, we’re assembling a very strong team with this goal in mind,” said Alves.
“I like to make history and this club has yet to win this title. I like big goals, ones that are special and ambitious and all that is why I am here.”
Alves lifted the UEFA Cup twice with Sevilla before winning a remarkable haul 23 of trophies in eight years at Barcelona.
“Believe me I came here to win trophies,” he added. “The club has grown amazingly and I’m delighted to be here.
“We’re going to share some great moments together, I’m sure of it!”
Alves will join a host of Brazilians in Paris, with Thiago Silva, Marquinhos and Lucas already at the Parc des Princes, while PSG president Nasser Al-Khelaifi said the recruitment of Alves sent a strong signal to their European rivals.
“You had a lot of opportunities but you chose our proposal, it’s a big message to the world,” Al-Khelaifi said of Alves’ decision to join PSG.
“We want to win lots of trophies, to win the Champions League, as everyone knows, is our biggest dream. With your experience, your ambition, I’m very confident about the chances of winning together.”
Alves’ arrival follows that of Spanish left-back Yuri Berchiche from Real Sociedad for a reported 14 million euros last week.