British media reported on Monday that Arsenal had accepted a 10 million pound ($13 million) fee for Szczesny, who spent the past two seasons on loan at AS Roma.
Szczesny featured in all 38 Serie A games for Roma last season and finished with 14 clean sheets, the most in the league.
The 27-year-old, capped 28 times by Poland, is expected to act as backup at Juventus for Italy's veteran number one goalkeeper, Gianluigi Buffon.
Szczesny made 132 appearances for Arsenal.
(Reporting by Hardik Vyas in Bengaluru; editing by John Stonestreet)
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