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Former Italy international Inzaghi left Lazio at the end of May after an impressive five-year spell in charge at the Stadio Olimpico, stepping in for Antonio Conte at Inter.
Sarri quickly emerged as a front-runner for the job and has been appointed on a two-year deal. The club shared a cryptic tweet hinting a deal had been struck with Sarri, who is known to enjoy a cigarette.
🚬— S.S.Lazio (@OfficialSSLazio) June 9, 2021
The 62-year-old has been out of management since being sacked by Juventus in August last year, paying the price for the Old Lady's shock Champions League elimination by Lyon in the last 16.
Nevertheless, Sarri did guide Juve to a ninth successive Serie A title, with his successor Andrea Pirlo unable to continue that run as the Bianconeri scraped a fourth-placed finish on the final day of the 2020-21 campaign.
Pirlo was then also fired, with Massimiliano Allegri returning to Juve.
Sarri boasts a win percentage of over 60 in each of his three previous roles and will be hoping to continue Inzaghi's fine work at Lazio.
The Biancocelesti finished lower than sixth only once under Inzaghi – though the sole campaign where they finished eighth, Lazio were able to console themselves with Coppa Italia success.
Lazio finished sixth in 2020-2021 but Sarri will hope to emulate their 2019-2020 season when it secured Champions League football by finishing fourth.
He will undoubtedly be keen to ensure the likes of Ciro Immobile, Joaquin Correa, Luis Alberto and Sergej Milinkovic-Savic stick around to aid their chances of a return to Europe's top table.