Baldé, 21, joined Hamburg's academy as a teenager and made 41 senior appearances for the club, scoring three goals and providing four assists, though he was never once on the pitch for a full 90 minutes.
His departure comes with two years still to run on a contract signed in 2024, meaning Strasbourg's fee — reported at up to €7m — represents a significant return for a player who managed only 16 appearances and three starts last season.
Announcing the move, he said: "As a Hamburg boy, it's your big dream to one day get to play at the Volksparkstadion and for HSV.
"I'm grateful and proud that I was able to fulfil that dream, and I want to sincerely thank everyone who accompanied and supported me along this journey."
Sporting director Claus Costa said the initiative to leave had come from the player himself: "Fabio came to us with the wish to leave his familiar surroundings in order to take the next step in his career."
Baldé, who is eligible for Portugal through family heritage and has represented the country's Under-21s, had reportedly grown frustrated at his lack of regular football, with fitness issues limiting his ability to force his way into Hamburg's plans on a consistent basis.
He was also involved in a dressing-room disagreement with team-mates Nicolas Capaldo and Yussuf Poulsen during pre-season training, after they challenged his effort levels — an episode that, in hindsight, marked one of the final signs of his time at the club coming to an end. He did not feature in a single pre-season friendly this summer.
Board member Kathleen Krüger described the sale as part of a broader academy strategy: "We have to continually develop our young players, so that we can either see homegrown talent playing at the Volkspark, strengthen the squad with them, or, in departures like Fabio's now, generate meaningful transfer fees."
For Strasbourg, who finished ninth in Ligue 1 last season, the deal continues a recruitment strategy built around promising young talent, following the loan arrival of goalkeeper Filip Jörgensen from parent club Chelsea. Baldé has signed a contract with the French club running until 2031.