Rose has signed a three-year contract and will take over the Cherries in the summer after Iraola announced he would leave the club at the end of the season.
The 49-year-old has been without a club since he was sacked by Leipzig in March 2025.
Rose's career in management started in 2012 and he has led a host of clubs also including Red Bull Salzburg, Borussia Monchengladbach and Borussia Dortmund.
In that time, he worked with some of football's current top players such as Erling Haaland, Jude Bellingham and Dominik Szoboszlai.
With Salzburg, Rose won two Bundesliga titles and the Austrian Cup and the DFB-Pokal and DFL-Supercup with Leipzig.
Bournemouth's appointment of Rose comes following Iraola's decision to leave the south coast when his contract expires at the end of term.
Spaniard Iraola was hired in June 2023 and has elevated the club to new heights in the Premier League.
Last season, Bournemouth finished ninth with a club record 56 points and reached the FA Cup quarter-finals.
Iraola has the side in a strong position again this season, with Bournemouth in eighth place during a 13-game unbeaten run and having a shot at European qualification.