The Gunners have made the 22-year-old their second signing of the summer window after Marquinhos's arrival from Sao Paulo and will pay an initial fee of €35m (£30m) for his signature.
The deal could rise to as much as €40m (£34.4m) with add-ons, and many believe that Arsenal have a gem on their hands with the Portugal Under-21 international.
Here, Sports Mole takes a closer look at Vieira's fledgling career so far and what fans can expect to witness from the creative hub.
Born in the Aveiro municipality of Santa Maria da Feira - about 20 miles south of Porto - Vieira was just eight years old when he first made the move to Porto's academy in 2008, and he quickly rose through the youth ranks.
The Portuguese first rose to prominence during his time in the youth team, as the midfielder started eight matches of Porto's triumphant 2018-19 UEFA Youth League campaign and even opened the scoring in the 3-1 final win over Chelsea.
The versatile Vieira also captained the academy side in next season's UEFA Youth League, while the 2019-20 Liga Pro season brought him seven goals and three assists from 23 outings, and he made his first-team bow in June of that year.
Vieira had already started to demonstrate his versatility by this point, featuring as a number eight, number 10 or second striker for the youth and B teams, and he scored two Primeira Liga goals from the right-hand side during his debut season.
Competent with the ball at his feet, as well as being a keen dribbler with an eye for goal and a tenacious attitude when pressing from the front, Vieira - who is not the most physically imposing at 5ft 7in - has earned early comparisons to compatriot Bernardo Silva, which has only led to greater excitement among Arsenal fans.
Vieira became a fully-fledged member of Sergio Conceicao's first-team squad in the 2020-21 season, but he found it difficult to make his mark at senior level and only had one goal and one assist to show from 29 matches.
The midfielder's solitary goal would come in a Champions League group-stage win over Olympiacos - only his second-ever appearance in the competition - but the contributions came rolling in last term.
Indeed, Vieira set up a whopping 14 goals in 27 Primeira Liga matches in 2021-22 to help Portugal wrestle the top-flight crown off of Sporting Lisbon's hands, and he also scored six himself.
Vieira provided a hat-trick of assists on more than one occasion in the domestic season - doing so against Moreirense and Belenenses - and his wealth of contributions came in spite of him starting just 15 Primeira Liga matches.
Only Benfica's Rafa (15) provided more assists than the ex-Porto man in the Portuguese top flight last season, and he also won the Taca de Portugal, but he was an unused substitute in the final against Tondela.
A regular of Filipe Ramos's during stints in the Under-18, Under-19 and Under-20 squads, Vieira has since been tearing it up with the Under-21s and has the all-time scoring record in his sights.
Largely featuring as a number 10 in the 2021 Under-21 European Championship, Vieira helped Portugal reach the final - which they lost to Germany - and he was named the Player of the Tournament after scoring one goal and setting up another.
The 22-year-old - who wore the captain's armband for the Esperancas earlier this year - has a total of 13 goals in 21 games for the Under-21s, as well as four assists.
Vieira is still waiting for his senior Portugal debut amid the intense competition for spots in the Selecao midfield, but it is surely only a matter of time before Fernando Santos considers him for a maiden cap.