Silva will be free to leave City at the end of their Champions League campaign later in August.
The 34-year-old is available after spending 10 unforgettable seasons at City. Qatari side Al-Sadd, where former Barcelona midfielder Xavi Hernandez currently coaches, were reportedly interested in signing Silva, but Lazio moved quickest.
Silva will join the Biancocelesti as they embark on their first Champions League campaign in 13 years. They qualified for Europe's top competition by finishing in fourth in Serie A, but for large parts of the season, they were competing for the Scudetto, going toe to toe with serial champions Juventus. Lazio fell flat after the season restarted in June, however, recording just five wins in their final 12 matches.
Widely regarded as one of the finest Premier League players of all time, Silva helped City become the juggernaut they are today. The Spaniard won four Premier League titles and tallied 60 goals and 93 assists in 309 top-flight appearances.
The Champions League is the only thing missing from Silva's glittering career, but he could yet lift the trophy later this month. City face Lyon on Saturday in a one-off quarterfinal in Lisbon. The tournament is following a single-elimination format due to the coronavirus pandemic.