The new kit deal, expected to land the north London club £60m-a-season for the next five years, will come into effect at the start of the 2019/20 campaign.
Adidas succeed Puma, who angered a large majority of Arsenal fans with their mundane designs for this season’s kits.
The Gunners will double their yearly kit sponsorship income with the switch, which should help bolster the club’s wage and transfer war chests.
Adidas created Arsenal’s jerseys between 1986 and 1994, and fans are yearning for the revival of retro-style kits.
Speaking to CNBC about the deal, Adidas CEO Kasper Rorsted said: “Last year was probably the worst season they had.
“And we believe that, in the long term, there’s so much upside in Arsenal.
“When we look upon the Arsenal brand, it’s such a stellar, global brand, that’s been underperforming the last couple years.”
Last term, in Arsene Wenger’s final campaign, the club clocked their joint-lowest Premier League point tally since the inaugural 1992/93 season.
Arsenal have also failed to qualify for the Champions League the last two years after playing in 19 consecutive editions of the competition.
Under the fresh leadership of Unai Emery, the club have recovered from two early losses and sit two points off the league summit, however.
“When it came up for us it was a no-brainer,” added Rorsted.
“The Premier League is the biggest commercial league in the world.
“We have Manchester United which is, commercially, the biggest club, and we really wanted a club in London.”
Following last weekend’s 5-1 thumping of Fulham, Rorsted joked: “They had a good weekend – but in the wrong kit!”