The 21-year-old Spain international has signed a five-and-a-half-year contract, which is understood to be worth an initial £46.7million, and a further £8.5m in potential add-ons. Barca have set a one billion euro (£841million) buyout clause into the deal.
Torres had hoped to be back in action for the Spanish Super Cup semi-final against Real Madrid on January 12, though his debut could be delayed after the Catalan club announced he had tested positive for Covid-19 along with team-mate Pedri.
A Barca statement on Monday evening read: "Pedri and Ferran Torres have tested positive for Covid-19. The players are in good health and are isolated at home."
Torres was presented at the Nou Camp on Monday morning, and spoke of having his focus set firmly on taking the LaLiga giants back to their former glories.
"I am facing this challenge with ambition, humility and a lot of desire," he said.
"When I left Manchester City I had the idea of coming back to LaLiga and Barca showed an interest.
"I am an ambitious player and I like a challenge. I want to take Barca back to where it belongs."
Torres signed for City from Valencia in the summer of 2020 for £20.9m, but spent just 16 months at the Etihad Stadium, scoring 16 goals in 43 appearances in all competitions.
The forward had made only seven club appearances this season, after breaking a metatarsal while on international duty during October.
Torres was not thought to be unhappy at City, with whom he won the Premier League last season and also helped reach the final of the Champions League.
"(City boss Pep) Guardiola is one of the best in the world and he played me in different positions," Torres said on Barcelona's website.
"I have learnt a lot from him at Manchester City and will take many nice memories of my time there.
"I can play across various positions and I will adapt well. I will play in the position that the (Barca) coach says, it does not matter to me which one he asks."
Barcelona president Joan Laporta is confident Torres can fulfil his potential at the Nou Camp.
"You are young, but you already have plenty of experience," Laporta said to Torres during the presentation.
"We knew about Ferran's situation and we were very pleased that he wanted to come to Barca so much. He is a great player."
Barca have been beset by financial difficulties in recent months, but were able to fund the Torres deal after securing a bank loan.
Director of football Mateu Alemany is confident there will be no issues in completing the formalities of the transfer.
"The truth of the situation is that when we signed Ferran Torres, we knew we did not have room in terms of salaries," Alemany said.
"However, we have been making moves in different areas and we are convinced we can register him."