The 31-year-old Brazilian is thought to have joined on a free transfer after agreeing personal terms and passing a medical.
Reds director of football Damien Comolli told www.liverpoolfc.tv: "We are delighted to sign Doni.
"It's a position we felt we had to strengthen because it will allow our young goalkeepers to go on loan and get some experience at some point during the season, which is crucial in their development."
Doni, who has 10 caps for his country, will provide back-up and competition for Liverpool number one Jose Reina, a role he also played at Roma behind Julio Sergio.
Comolli said: "We are getting a very experienced goalkeeper who is used to handling the pressure of big games and international matches with Brazil. He had a very good end of last season with Roma, so we are very pleased.
"When you come here and know you will be a number two behind Pepe, what's important for us is the attitude and mentality off the pitch and in the changing room.
"He's got to be supportive of the number one but also be aggressive enough to push the number one on a daily basis, and I think Doni represents all that.
"When we approached him the first time, obviously he wanted to be a number one somewhere, but he said Liverpool Football Club is such a big club that if he wanted to come as a number two then he would come."
The director of football, meanwhile, revealed he sounded out Liverpool midfielder Lucas Leiva about his fellow Brazilian before pursuing the deal.
"I spoke to Lucas about Doni and he was very complimentary about him as a person and as a goalkeeper, so I think it's a great deal for us," added Comolli.
"He is suited to English football. He is big and good in the air and his distribution is quick as well. When you play for Roma for years and years, the pressure at that club in that city is tremendous, so the fact he can handle that shows he can take anything."
Doni, who holds an Italian passport, joined Roma in 2005 from Brazilians Juventude and spent six seasons with the Giallorossi, winning the Coppa Italia in 2007 and 2008.
The 31-year-old is Liverpool's third summer signing following the capture of Jordan Henderson from Sunderland and Charlie Adam from Blackpool, while a fee has also been agreed for Aston Villa winger Stewart Downing.