The Swiss international, a right-back, will join the club on July 1 when his contract with the German club expires, and is likely to provide stiff competition for Steve Finnan and Alvaro Arbeloa in the full-back role.
"Philipp is still young but has gained great experience from playing in the Bundesliga with Borussia Dortmund and on the international stage with Switzerland," said Benitez. "He also played in the Champions League during his time with Basel and so is used to top level football.
"He is an offensive player with great energy and a winning mentality. His strength is going forward and I am confident he will prove to be a quality addition to our squad."
Degen had little hesitation in committing himself to the Reds.
"When I received the offer from Liverpool, there was no doubt I would accept it," he said. "They are one of the biggest clubs in the world and I am looking forward to the challenge of establishing myself there and playing in the best league there is."