The Estonia international played only an intermittent role in Liverpool's 2018-19 exploits, with the arrival of Virgil van Dijk pushing him further down the pecking order in January.
Klavan made a total of 28 appearances over the course of the season as Jurgen Klopp's men battled to a fourth-placed Premier League finish as well as a spot in the Champions League final.
Liverpool's squad contains plenty of players with experience in Italy's top flight, and Klavan has confirmed that their recommendation pushed him towards Italy.
"I had offers from several teams, including in other countries, but Cagliari really wanted me," he explained to Sky Sport Italia.
"Darijo Srna advised me to come here, as I talked to him via Dejan Lovren. Other Liverpool teammates like Alisson, Salah and Lucas Leiva all spoke highly of Serie A.
"I’m certain we’ll do great things here and I am really fired up. The city is wonderful and so are the fans, I can’t wait to get started."
Klavan, who has made more than 500 appearances during a career that has taken in spells in Germany, Netherlands, Norway and England as well as his native Estonia, is now tasked with cementing Cagliari's place amongst Italy's elite after the Sardinians narrowly avoided relegation from Serie A last season, finishing four points clear of 18th-placed Crotone to assure survival.