Paris Saint-Germain's Spanish headcoach Unai Emery is pictured before the French cup semi-final match between Caen (SMC) and Paris Saint-Germain (PSG) on April 18, 2018 at the Michel-d'Ornano stadium in Caen, northwestern France.
Emery emerged as the unanimous choice following a recruitment process in which all candidates were spoken to.
Manchester City first-team coach Mikel Arteta had been a front-runner to replace Wenger, with City boss Pep Guardiola giving the former Arsenal captain his blessing to pursue a career in management at the Emirates.
An announcement is expected later this week.
Emery, who was at one stage a 66/1 shot and behind Tim Sherwood in the betting odds to become Arsenal manager, "is not completely fluent" in English, but that will not be a problem.
His time at PSG, where he won the French title this season, had been less successful, with the club's Qatari owners choosing to replace him with former Borussia Dortmund coach Thomas Tuchel after two disappointing campaigns in the Champions League.
Arsenal chief executive Ivan Gazidis, Raul Sanllehi and recruitment chief Sven Mislintat led the Gunners' search for a new boss and decided on Emery.
What's going on at Arsenal?
Wenger's successor will be charged with trying to restore Arsenal to regular Champions League qualification and Premier League title contention, the Gunners having now missed out on elite continental competition in back-to-back campaigns. If we do see a difference in intensity, drive and consistency everybody will get onside and that's all Arsenal fans want to see.