The Greek defender has spent the last two seasons with the Bundesliga outfit, who dramatically sealed their top-flight status for another season with a last-gasp goal to beat Cologne.
Reports had suggested a permanent move to the Mercedes-Benz Arena for the 24-year-old was dependent on Pellegrino Matarazzo's men staying in the top division of German football.
The Athletic reports while an obligation to buy if Stuttgart secured their Bundesliga status was written into the loan contract, the German side had already told Arsenal weeks ago they wanted to complete a permanent deal regardless of where they finished.
The report adds that Stuttgart - who paid an initial loan fee of £500,000 to sign Mavropanos - will now fork out another £3m, with bonuses worth up to another £1.5m.
The fee is considered low due to the attention the Greece international has received since moving to Germany, with Borussia Dortmund and West Ham reportedly having kept tracks on him.
But the same outlet adds the £4.5m will be paid to Arsenal up front, handing the Gunners a tiny boost ahead of what promises to be another busy transfer window in north London.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!