Juventus announced his capture on Wednesday:
The Evening Standard's James Benge reported the fee ahead of his medical in Turin.
The Poland international has spent the last two seasons on loan at Roma after leaving the Gunners in search of regular first-team football following the arrivals of David Ospina and Petr Cech at the Emirates Stadium.
While he didn't always convince at Arsenal, the 27-year-old has gone from strength to strength in Serie A and enjoyed two strong campaigns with the Giallorossi.
GianlucaDiMarzio.com's David Amoyal had one word to sum up his efforts last season:
While he's not likely to unseat the legendary Gianluigi Buffon in Turin, the Italian is 39 and has just one year left on his contract with the Bianconeri, per ESPN FC's Ben Gladwell.
Szczesny could be allowed games in cup competitions this season and perhaps the occasional league match if manager Max Allegri wishes to rest his side ahead of a crunch European clash.
Should Buffon hang up his gloves next year at 40, Szczesny would then be in place to take over as the Old Lady's No. 1.
The stopper isn't at Buffon's high level—very few goalkeepers are, even now—but his form at Roma has perhaps earned him the chance to prove he can be an effective replacement.
According to Squawka, only Gianluigi Donnarumma of AC Milan statistically outperformed Szczesny in Serie A last season, while his record of 14 clean sheets was the best in the league, two more than the 12 Donnarumma, Napoli's Pepe Reina or Buffon managed.
Szczesny's career prospects have improved since his departure from Arsenal on loan in 2015, and with his move to Juventus he has gone up another level still.