Arteta officially began work at Emirates Stadium on Sunday after agreeing a three-and-a-half-year deal to succeed Unai Emery.
Arsenal head of football Raul Sanllehi said he and technical director Edu spoke to "several top-class candidates," one of which was rumored to be Vieira.
💬 "We met several top-class candidates, and Mikel stood out to every single one of us as the perfect person for us."— Arsenal (@Arsenal) December 22, 2019
Head of football Raul Sanllehi and technical director Edu discuss the process behind appointing @m8arteta 👇
Former Gunners captain Vieira was linked with the role throughout the recruitment process but, in an interview with Canal Football Club, claimed there was no substance to the speculation.
Asked if he had been contacted, Vieira – who has also been linked to David Beckham's MLS franchise Inter Miami – said: "No. It's flattering seeing your name everywhere but I am under contract with Nice.
"I have known since I arrived how lucky I am to be involved with this club's project.
"I don't have any intention or desire to go and look elsewhere."
The 1998 World Cup winner said qualifying for Europe was part of his long-term plan for the club.
"The objective is to play in the Champions League one day, but it will take time," he said.