The Portuguese midfielder is the Premier League club's first major signings of the summer transfer window following the arrival of goalkeeper Matt Turner and Brazilian striker Marquinhos.
Vieira, 22, said he was "incredibly proud" to join a "great and historic" club like the Gunners. The deal includes £4 million of achievable performance-related add-ons.
He said: "I was born near Porto and played for Porto since I was eight. I have always admired the way Arsenal play.
"There were a lot of players over the years that I remember very well:" (Dennis) Bergkamp, (Cesc) Fabregas, (Santi) Cazorla, Thierry Henry
"Arsenal is a huge and historic club. I am delighted to be here and I cannot be prouder
Manager Mikel Arteta said: "I am delighted that we have found and signed such a great talent.
"Fabio is a very creative player who will bring quality and versatility to our attacking game.
"We welcome Fabio and his family to our club and look forward to working with him ahead of the new season."
Vieira, who shares his name with legendary former Gunners midfielder Patrick Vieira - now the manager of Crystal Palace - will wear the number 21 shirt.
He added: "It's a big step in my career. It's of course a quick process. That's what attracts me. Meeting people at the club is really positive for me. I love it here, I'm in Everything is given here for the team.
'
I'm an attacking player who looks to find space between the lines, to be able to finish off moves either with assists or by scoring goals. I think those are the main attributes that Arsenal fans can expect from me.'
Technical director Edu continued: '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.'
.png)