Klose put pen to paper after his contract with Bayern Munich expired.
"I cannot help but be happy and satisfied with this signature," Reja told Radio Lazio Style.
"Our intention is to bring players with international experience and quality to Lazio. In those respects, Klose is a guarantee.
"I had spoken to Miro a month ago, as he wanted to know our style of football. He said that he was very happy to come to Rome.
"President Claudio Lotito did very well to close to deal, as Klose had several different offers on the table. He kept his word, as he told me that he only wanted Lazio and that proved to be the case.
"Klose wants to challenge for a place in the Euro 2012 Germany squad and knows he can make an impact with us.
"I'm sure it won't take him long to settle in, as he will become a part of a squad that is already very strong and united."