The 34-year-old Frenchman was available on a free transfer after his contract with Sunderland was terminated and he arrives to soften the blow of losing the German for two months
The Germany international has been ruled out of action for up to two months after picking up a knee injury and, with the Frenchman's contract at Sunderland having been terminated in January, he joins the Biancocelesti for free.
The 34-year-old has signed a deal until the end of the season and he will reportedly earn around €500,000 (£431,000) during his time in Rome, but he is most pleased about signing for one of Italy's main clubs.
"I am very happy to be here at this big club," he told reporters. "I have found a great group and working with them will be a real pleasure for me.
"I want to give my best. I am here to help the team during this injury and I'm happy to do it.
"I know on Saturday it will be a big game against Napoli and I am here to help. In life you must always try to give your best. I am a very competitive person, so the important thing is to always do better.
"This is a great team and a great country - I am happy to be here."
Club president Claudio Lotito highlighted Saha's experience from clubs such as Manchester United as effective motivation for the side currently occupying third place in Serie A.
"Saha is a person who can give a great contribution to this club," he told reporters.
"His history speaks for him and he has come to Lazio with great motivation," he continued. "He can help us reach our objectives as we deal with a few injuries.
"He is not the only new signing, as we have already secured Colombian Bryan Perea for next season."
Lazio head coach Vladimir Petkovic was also present and was quick to dismiss any suggestions that the Frenchman has been brought in as a replacement for Klose.
"Saha is not just a replacement for Klose," he added. "When the German returns, we will have more options available to us. His arrival makes us even more competitive."