The Cherries sacked manager Gary O'Neil on Monday despite the former midfielder guiding the Premier League club away from relegation and securing a 15th place finish.
Spanish boss Iraola was on Leeds' list of contenders after Jesse Marsch was axed and recently a free agent after leaving Rayo Vallecano.
"We're so excited to welcome Andoni to the club," AFC Bournemouth owner and chairman Bill Foley said. "With his contract in Spain coming to an end this summer we wanted to act quickly.
"He was highly sought after by other clubs across the continent, and his style of play has been an important factor in making this decision. His achievements in Spain have certainly been very impressive, and we're confident that he is the right man to lead our next chapter.
"We have identified a number of targets in the transfer market, which along with our January additions will supplement our strong playing squad to give Andoni the best chance to consolidate our Premier League status and keep progressing."
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talkSPORT understands Bournemouth wanted Iraola last Autumn but could not lure him from Rayo Vallecano during the season.
Bournemouth owner Foley made the decision to sack O'Neil as he wants to go in a new direction and to implement a new style of football.
talkSPORT understands Foley is ambitious to progress quickly and sees Iraola as a manager with a clear identity that suits the club, the current squad and summer targets.
Iraola does not have previous Premier League experience, having managed AEK Larnaca, Mirandes and Rayo Vallecano.
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The 40-year-old left Rayo Vallecano at the end of this season after turning down a renewal offer.
At the moment, O'Neil's backroom staff will remain in place at the Vitality Stadium.
The former Middlesbrough star had triggered an extra year on his contract after keeping them up and turned their season around following a rocky start under Scott Parker.
But the Cherries will now have a different manager in the dugout for the 2023/24 season after a rollercoaster day.