Romagnoli 27, made 247 appearances and scored 10 goals in all competitions in his seven years at champions AC Milan.
AC Milan bid their skipper farewell on Twitter with the caption, "Captain of many battles: our tribute to Alessio Romagnoli as we bid him farewell".
The skipper will miss his former side's return to Europe's elite competition the Champions League after their automatic qualification by winning the Scudetto.
He will still be able to participate in European competition given Lazio's 5th place finish last season which qualifies them for the Europa League.
Romagnoli also represented Italy 12 times, and joined AC Milan from Lazio's local rivals AS Roma in 2015 after spending a year on loan at Sampdoria.
Spanish side Valencia said on Tuesday they had signed another AC Milan player, winger Samu Castillejo, on a contract until 2025.