Sarri, who led Chelsea to the 2019 Europa League title, has been out of work since being sacked by Juventus in August, despite guiding the Turin club to the Serie A title in his only season in charge.
He replaces Simone Inzaghi, who won three trophies in five years at Lazio before leaving for Inter Milan.
Lazio teased the announcement with a tweet of a cigarette emoji.
Sarri, 62, is famous for smoking on the touchline during games.
His career has been an interesting one, having been a banker as well as managing low-level Italian clubs for the first decade of his coaching career.
He quit his day job to focus on management in the early 2000s, but did not reach Serie A until 2013-2014, at the age of 55, when he led Empoli to the top flight.
Since then he has managed Napoli, Chelsea and Juventus – the latter two for just one season each.