Porto said last week they had agreed a 40 million euros ($42.11 million) deal with Arsenal for the transfer of Vieira.
Porto added that Arsenal would pay an initial 35 million euros with a further five million dependent on Vieira achieving certain targets at the London club.
The 22-year-old scored seven goals and made 16 assists from 39 appearances in all competitions last season as Porto won the league and Cup double. He also represented Portugal at the Under-21 level, scoring 13 goals in 21 appearances.
"Fabio is a very creative player that will bring high quality and versatility to our attacking play," manager Mikel Arteta said in a statement.
Vieira follows Brazilian forward Marquinhos and American goalkeeper Matt Turner in joining Arsenal during the close season.
Arsenal finished fifth in the Premier League last season and were beaten to the final automatic Champions League spot by north London rivals Tottenham Hotspur.