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Thestrup, 24, becomes the club's third addition of the summer so far - following Monday's announcements of the arrivals of international players Kaja Erzen and Andressa Alves.
"I cannot wait to move to your magnificent city and start the season with AS Roma," Thestrup said.
A quick, technically-adept forward, Thestrup spent the past two seasons at Ballerup-Skovlunde Fodbold.
During the 2018-19 campaign she scored 17 goals in 24 appearances for the club, finishing second top goalscorer in the league as BSF finished fourth.
She previously spent three years at Brondby, as the club won the league on two occasions, and has been capped at full international level by Denmark.
Betty Bavagnoli's side finished fourth last season in Serie A, in what was the club's first-ever professional campaign.
Welcome to Rome, Amalie!
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