The 43-year-old replaces Dutchman Arne Slot, who led Liverpool to the EPL title in his debut campaign but was sacked after failing to live up to expectations in his second season.
"You don't need a lot of things to get attracted by Liverpool. Liverpool is Liverpool," Iraola, who is reported to have signed a two-year contract, said in a statement.
"But obviously the atmosphere, the supporters, the club, the players, the chance for me to coach top-level players, the chance to fight for titles. I think it cannot be more attractive than this. It's difficult to find it. So, really excited to start."
Iraola, a former Spain international who played for Athletic Bilbao between 2003 and 2015, took charge at Bournemouth in 2023 and oversaw a significant upturn in the club's fortunes.
In the 2024-25 season, Bournemouth recorded a points total of 56 and finished in ninth place, their joint-best top-flight finish at the time.
The Spaniard, who announced his departure from the south-coast club in April, bettered that finish this season, guiding Bournemouth to sixth place and sealing qualification for the Europa League. The y finished just one place and three points behind Liverpool.
The Merseyside club qualified for next season's Champions League despite finishing the EPL season with 60 points - their lowest tally since 2015-16 and a distant 25 points behind winners Arsenal.
Liverpool did consider other candidates but Iraola was the primary target following Slot's sacking last weekend, and the club moved swiftly to tie up a deal for the former Bournemouth manager, who had already spoken to Crystal Palace, Bayer Levekusen and AC Milan.
At Bournemouth, Iraola garnered praise for implementing a high-pressing and progressive style of football, centred around attacking swiftly.
That approach would see him fit in well at Liverpool, who were renowned for their high-octane brand of football under Klopp, a style that Anfield icon Mohamed Salah urged the Merseyside club to revive before his departure.
Iraola now faces the difficult task of resuscitating a side who stumbled to a fifth-placed finish last season, while also having to contend with the absence of Salah, who had been Liverpool's main source of goals for the better part of the past decade.
