The 22-year-old made 13 Championship appearances for the Potters, scoring once in a 3-1 victory at Swansea City.
Albion's pathway development manager David Weir said, “Leo has made excellent progress during his loan spells in the second tier in Germany and here in the Championship, with Coventry and Stoke, but this gives him the chance to play at the top level.
“It is an excellent opportunity to play in the top division of Italian football, against some of Europe's top teams, and we will be monitoring his progress out in Italy.”
Ostigard signed for Albion from Molde in 2018, before spending the 2019/20 campaign on loan with German second division side St Pauli.
That was followed by a successful 2020/21 campaign with Coventry City, where he helped Mark Robins’ side maintain their Championship status having returned to the second tier after an eight-year absence.