The forward had failed to break into the first team at the Stadium of Light after joining the club in the summer of 2011 and was released on a free transfer last month following spells at Everton, Tottenham, Manchester United and Fulham during over a decade of playing in the Premier League.
"I am very happy to be here at this big club," the striker told reporters at a press conference on Wednesday.
"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 [Klose’s] 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."
Biancocelesti president Claudio Lotito was quick to praise the 34-year-old, and also hinted that he would play a big role in the second half of the season.
"Saha is a person who can give a great contribution to this club," said Lotito.
"His history speaks for him and he has come to Lazio with great motivation. 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."
Klose was ruled out for around two months with a knee injury and head coach Vladimir Petkovic believes Saha will give the Italian side options even when the striker comes back to the first-team fold.
"Saha is not just a replacement for Klose," said Petkovic. "When the German returns, we will have more options available to us. His arrival makes us even more competitive."