The 24-year-old has been at the Emirates since 2011 but has spent much of his north London tenure out on loan.
Indeed, the Costa Rica international has previously undergone spells with Lorient, Real Betis, Olympiacos and Villarreal – winning the top flight title with the Greek outfit during 2013/14.
Meanwhile, Campbell has made 40 appearances across all competitions for Arsene Wenger’s side, scoring four times – including three Premier League goals last season.
He’ll now spend the 2016/17 campaign with Sporting Lisbon, who are expected to be a part of the Primeira Liga title race this term.
The deal is still subject to international clearance but Arsenal appear confident it will go ahead, having announced Campbell’s move via their official website.
The winger-forward has already picked up 55 caps for Costa Rica and featured prominently in the side that impressed at the 2014 World Cup.