The move was officially confirmed by the Gunners' online store Arsenal Direct after the club agreed a €40m (£34.4m) deal to bring the 22-year-old to the Emirates Stadium from his homeland.
Arsenal's announcement soon followed, in which they confirmed that Vieira had signed a 'long-term contract' at the club, which is believed to be a five-year agreement.
Porto revealed last week that a deal was in place for Vieira to join Mikel Arteta's side, and the Portuguese champions will receive an upfront fee of €35m (£30m).
Vieira has been given the number 21 shirt at Arsenal, which was previously worn by Calum Chambers before his January departure to Aston Villa.
Speaking to arsenal.com after Vieira's capture, technical director Edu said: "We're so pleased to have completed the signing of Fabio from FC Porto. Fabio is a player with special qualities who is comfortable with the ball in the final third of the pitch.
"We are all looking forward to working with him and enjoying his future contribution to Arsenal. We will now continue to work hard and are looking forward to finishing this transfer window as strongly possible."
Manager Arteta added: "I am very excited that we have identified and signed such a special talent. Fabio is a very creative player that will bring high quality and versatility to our attacking play.
"We welcome Fabio and his family to our club and are looking forward to starting work with him ahead of the new season."
During his announcement video, Vieira spoke of his pride at playing for a "huge and historic club", saying: "I've always admired the way Arsenal play.
"There are many players who I remember well from over the years: Dennis Bergkamp, Cesc Fabregas, Santi Cazorla, and Thierry Henry. Arsenal are a huge and historic club. I'm so happy to be here, and I couldn't be prouder."
After rising through the youth ranks at Porto, Vieira went on to score 10 goals and provide 18 assists in 76 games for the club, winning two Primeira Liga titles, one Taca de Portugal and the UEFA Youth League in 2019.
The 2021-22 Primeira Liga season saw Vieira score six goals and provide 14 assists in 27 matches - second only to Benfica's Rafa (15) - with no other player aged 21 or under setting up as many goals in Europe's top leagues last term.
The versatile midfielder is yet to make his senior debut for Portugal, but he has 13 goals and four assists to boast from 21 Under-21 matches and was named the Player of the Tournament at the U21 Euros last year.
Vieira becomes Arsenal's second signing of the summer transfer window after the capture of Marquinhos from Sao Paulo. body check tags ::