Vieira has arrived at the Emirates Stadium for a fee of £34m on a long-term contract.
The 22-year-old is Arsenal's third summer signing following the arrivals of Brazilian Marquinhos and goalkeeper Matt Turner from America's Major League Soccer.
Vieira came through the FC Porto youth ranks before graduating to the first team.
He scored six goals and provided a league-high 14 assists in 27 appearances as FC Porto won the Portuguese league last season.
Arsenal boss Mikel Arteta said: "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."
"Fabio is a player with special qualities who is comfortable with the ball in the final third of the pitch," added Arsenal technical director Edu.
"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."
Vieira is yet to be capped at senior level by Portugal but won player of the tournament at last summer's European u-21 Championship.
"This is an important step forward in my career," Vieira told the club's official website.
"It certainly was a fast process. It was something that I was drawn to. Meeting the people at the club was a real positive for me. I'm loving it here and I'm here to give the team my all.
"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."
