Doni was a team-mate of Riise at Roma and sought the former Red's advice when he first heard of Kenny Dalglish's interest in him.
"I spoke a lot about Liverpool with John and he told me what a special club it was," said the goalkeeper.
"He spoke about the supporters, the way Liverpool play and this is a very big challenge for me.
"I couldn't turn down the opportunity to come to the Premier League, especially signing for Liverpool which is a huge club in Europe."