The 24-year-old is set to make the switch from Sweden to Italy's Serie A in a deal worth €2.5 million, according to Transfer Journal's Nicolo Schira.
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The current Mjällby man is expected to sign a deal with Cagliari that will run until 2030, with the option to extend for a further year.
Stroud has impressed at the World Cup this summer, and featured in all of Sweden's matches so far at the tournament, having also started in the 1-1 draw against Japan.
Alongside his performances at this summer's WC, Stroud has scored 23 goals in 98 games for Mjällby since joining in 2023.
He has also won the the Allsvenskan and the Swedish Cup with Mjällby, and is expected to add quality and versatility to Fabio Pisacane's Cagliari squad.