The 29-year-old has joined the club on a free transfer from Atletico Madrid, as his contract with the Spanish side was due to expire in the summer.
Reds boss Benitez told the club’s official website: “We were looking for players with character and a good mentality.
“He has played for Argentina and Atletico Madrid and is a player with personality.
“He can play in three positions – on the right, left or as a second striker – and is someone with a very positive mentality, which is what we are looking for.
“He is comfortable on the ball, can pass and keep possession. He is good at getting into the box and scoring goals and a good finisher. Every year he gets five to 15 goals from the right side of midfield.
“I know he was not doing as well as he did in the past at Atletico Madrid, but he is doing really well with Argentina and wants to impress for the World Cup.”
“He knows Mascherano and Torres and he can provide a lift for some players,” said the Liverpool boss.
“I think he will adapt to English football because he is a clever player and takes up good positions on the pitch.
“It is a question of adjusting to the pace of the game and he will need some time, but with these players around it will be easier for him.”
Benitez added: “Rodriguez will be a different kind of player for us and also competition for Dirk Kuyt on the right side, along with Nabil El Zhar and Yossi Benayoun.
“He will give us the opportunity to manage some of the other players and rest them if necessary to keep the level of the team.
“I have been talking with him and he is really pleased and ready to come here. I have told him what we are expecting from him and he is ready for the challenge.”