Bogdan effectively replaces Brad Jones, who was released at the end of his contract, but unlike Jones, the Hungary international does not intend to spend his time at Anfield as back-up to Simon Mignolet.
“I think it’s a massive challenge,” Bogdan said of his battle with Mignolet to be first choice.
“I know him as a keeper, I’ve been watching him and we are a very similar age.
“I respect him as a keeper. I haven’t had a chance to meet him yet, but I’m sure we’re going to get along very well and we’re going to have a good relationship.
“We’re going to compete, of course, that’s the nature of this position and the sport. It’s going to be a big challenge but at the same time we are going to help each other as well.
“I want to play as many games as I possibly can and be a No 1 keeper for Liverpool. I have to prove myself and prove to the manager that I’m able to do that.
“I would like to win trophies. I’m really excited to join a club where I have a chance to do that. It’s a massive step in my career and I’m looking to enjoy it.”
Bogdan joins Liverpool after eight years at Bolton but admits it was an easy decision to make to move to Anfield.
“I couldn’t sleep for two days. It still hasn’t sunk in properly yet,” he told Liverpool’s official website.
“On one hand, it was an easy decision of course. I’m playing for one of the most famous, if not the most famous club in the world, playing in Europe and challenging for titles. But on the other hand, I played for Bolton for eight years. I loved the club and thank them a lot. So that was hard, but not in professional terms.
“Bolton was the club that made my dream come true – playing in the English Premier League. Ever since I was a boy that was the only thing I could think about, to play in the English Premier League. I did that with Bolton and I’ll always keep them in my heart.”
Liverpool completed the signing of England right-back Nathaniel Clyne from Southampton on Wednesday and will now focus their attention on Aston Villa Christian Benteke, although there have been no further progress in negotiations with the Midlanders, according to the Liverpool Echo.