The former Bournemouth boss has signed a two-year contract at Anfield and replaces Arne Slot, who was sacked last weekend just a year after leading the Reds to the Premier League title.
Iraola told Liverpool's website: "Really excited, really excited. Because obviously you know about Liverpool, you know that it's a big club, a massive club, one of the biggest in the world.
"But feeling inside and understanding a little bit more of this club, I always thought it's a special club.
"You don't need a lot of things to get attracted by Liverpool. Liverpool is Liverpool.
"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.
"I can only say [to the fans] that I want to become one more of you, I want to earn the right to be one of you, so we can enjoy it all together."
Iraola impressed during three seasons in charge of Bournemouth, leading the Cherries to European qualification for the first time in their history last term as they secured a spot in the Europa League with a sixth-placed finish after ending the campaign unbeaten in 18 matches.
The Reds feel that the Spanish coach is ideal to implement an aggressive and attacking style of football, although the club's former defender Jamie Carragher says there are "question marks" as to whether he can succeed at Anfield.
The Sky Sports pundit said: "He's done a brilliant job in the Premier League, what Bournemouth have done is absolutely fantastic, but there are still huge question marks.
"The way he plays is definitely the way Liverpool want to go back to: high-intensity football. We know he's fantastic at that, but it's not just all about that when you're the Liverpool manager.
"Off the ball was a big problem for Arne Slot, that was the thing that really worried me, and I said all season that Liverpool off the ball were so poor.
"That's a big part of Liverpool's DNA, not just under Jurgen Klopp. The reason we talk about the Anfield factor, a lot of it is off the ball, not just on it, so he's fantastic at that.
"My worry is, can you play at that intensity when you're playing every three days, and that was only getting played once a week with Bournemouth. That is completely different.
"Whenever you're bringing a manager in for a top club in England, you're thinking: 'Can he win me the league?' That's a big question mark around him, or any manager coming in, but Liverpool had a manager who's won the league, so that's why I was always torn."
