The German has agreed a three-year deal.
Iraola revealed last week he will leave the Cherries when his contract expires at the end of the season, bringing an end to a successful three-year reign.
Despite hoping to extend the Spaniard's stay, Bournemouth were prepared for that scenario and have moved quickly to appoint his replacement as part of their long-term project.
"AFC Bournemouth is delighted to confirm the appointment of Marco Rose as the club's new head coach on a three-year contract, which will begin following the conclusion of the 2025/26 season," read a club statement.
"The 49-year-old arrives on the south coast with a wealth of experience at the highest level of European football."
Rose has been without a club since he was sacked by RB Leipzig in March 2025 and previously managed RB Salzburg, Borussia Monchengladbach and Borussia Dortmund.
He has a track record of player development, having worked with the likes of Erling Haaland, Jude Bellingham and Dominik Szoboszlai during his career.
Bournemouth's owners were attracted by the 49-year-old's high-pressing, attacking style of play, which they believe aligns with the club's identity.
The departing Iraola, 43, arrived in Dorset on an initial two-year deal in June 2023, taking over a side which finished 15th under Gary O'Neil.
He guided Bournemouth to 12th, then ninth, achieving club record points totals each season. They are currently eighth.
Iraola has been linked with a return to former team Athletic Bilbao, as well as the Manchester United job.
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