The German newspaper claims the deal has been “fixed” for some time, but the Gunners were waiting for manager Arsene Wenger’s future to be tied up before confirming the transfer.
It is said the Bosnian left-back, 23, will join the North Londoners when his contract at Schalke runs out at the end of this month, and the switch is set to earn him around £7.5million-a-year.
Wenger is looking to strengthen his full-back options this summer, after Nacho Monreal and Kieran Gibbs both failed to convince in the 2016/17 campaign.
Kolasinac, 23, is also effective going forward and can even play in left-midfield, so he would be perfect if the Frenchman opts to employ a 3-4-3 formation next term.
He was a mainstay in Schalke’s back line this season, playing 36 league and cup games, scoring three goals and providing an impressive nine assists.
The 23-year-old made the step up into the club’s senior set-up in 2012, and he has since made 123 appearances in all competitions for the side.
Kolasinac has been capped by Bosnia and Herzegovina 23 times, most recently appearing in his side’s 5-0 World Cup qualifying win over Gibraltar in March of this year.