The north London club secured the title without kicking a ball after Manchester City's 1-1 draw away to Bournemouth left Mikel Arteta's side with an unassailable four-point lead at the top of the table heading into Sunday's final round of fixtures.
As thousands of supporters flooded the streets around the Emirates in celebration, former Arsenal manager Wenger - the architect of the club's last title-winning side in 2004 - delivered a heartfelt tribute to the current squad.
"You did it," Wenger said in a video released by Arsenal on social media. "Champions go on when others stop. This is your time. Now, go on and enjoy every moment."
Wenger won three Premier League titles during his legendary spell in charge, including the famous unbeaten "Invincibles" campaign, but Arsenal had endured years of frustration since their last triumph, finishing runners-up in each of the previous three seasons.
Former striker Wright was among the most visible figures during Tuesday's celebrations, joining fans outside the Emirates as chants and fireworks lit up the night.
The ex-Arsenal forward, a hero of Wenger's early years in charge, helped whip supporters into a frenzy as celebrations continued long after confirmation of City's dropped points filtered through.
Inside Arsenal's London Colney training ground, the squad gathered together to watch City's match before erupting into celebrations of their own.
The celebrations stretched into the early hours of Wednesday morning, with Bukayo Saka, Declan Rice, Jurrien Timber and Crystal Palace winger Eberechi Eze spotted outside the Emirates at around 5 am taking photographs with supporters.
The title triumph also drew congratulations from across football and beyond.
Prime Minister Sir Keir Starmer, a lifelong Arsenal fan, wrote on X: "22 long years for the Arsenal. But finally, we're back where we belong. Champions!"
Arsenal will officially lift the Premier League trophy after Sunday's final-day trip to Crystal Palace, but Arteta's side could yet crown their season with an historic double when they face Paris Saint-Germain in the Champions League final on May 30.
Gabriel Martinelli has admitted Arsenal's run to the UEFA Champions League final has been one of the biggest moments of his career, as the Brazilian winger prepares for Saturday's showdown with Paris Saint-Germain in Budapest.
Arsenal manager Mikel Arteta could lead his side to the greatest achievement in the club's history if they complete an extraordinary double by winning the Champions League this weekend.
Paris Saint-Germain are on the brink of football history as they prepare for the UEFA Champions League final against Arsenal, with manager Luis Enrique leading a side now aiming to defend their crown and cement a new era of dominance in Europe.
Tottenham's hierarchy has admitted that consecutive 17th-place Premier League finishes represent a major failure, with majority owners ENIC and the Lewis family pledging a sweeping rebuild to restore the club's fortunes.
