Giroud has signed a contract with the Rossoneri – said to be for two years – after they met the modest release clause in his contract.

Chelsea triggered a one-year extension for Giroud last season, which meant a free transfer was not possible, but there were otherwise few obstacles to block the move.

Giroud was rarely a first-choice option at Chelsea after his arrival from Arsenal in January 2018. He found starts particularly hard to come by after the appointment of Thomas Tuchel.

After the German replaced Frank Lampard as coach in late January, Giroud made only three Premier League starts, none of which came after 28 February.

Previously, under Lampard, Giroud had taken on a fairly important role after the three-month coronavirus-enforced pause, scoring six goals in seven starts.

The signings of Timo Werner and Kai Havertz restricted Giroud from building on that form at the start of 2020-2021 – he did not score a Premier League goal until December, though he did net five times in the UEFA Champions League group stage.

That included a remarkable four-goal haul in Chelsea's 4-0 win away to Sevilla, which made him the oldest player (34 years, 63 days) to score a hat-trick in the UEFA Champions League/European Cup since Ferenc Puskas (38 years, 173 days) for Real Madrid in 1965.

Although Giroud did not feature for Chelsea in its UEFA Champions League semi-final or final matches, he did get a medal in the competition and heads to AC Milan as a European champion.

Giroud will hope he enjoys a resurgence similar to his new team-mate Zlatan Ibrahimovic in Milan, with the Swede scoring 15 goals in just 19 appearances last term before sustaining an injury.

French FIFA World Cup winner Giroud is the second player to swap Stamford Bridge for San Siro this year, after Fikayo Tomori to Serie A after his loan move was made permanent.

On top of Giroud, Milan is close to two other incomings, with Brahim Diaz, who spent last season at San Siro on loan from Real Madrid, set to rejoin on a two-year deal from Los Blancos, with an option to buy.

Monaco left-back Fode Ballo-Toure, meanwhile, is also set to sign.