The 37-year-old Frenchman, who helped Milan to the Serie A title in 2022, is leaving after three years and will join Los Angeles FC.
Giroud was given a standing ovation when he was substituted off six minutes from time, hugging all of his teammates and coach Stefano Pioli as the crowd sang his name.
Milan's last match of the season was also Pioli's final match in charge, bringing to an end a five-year stint that included the Champions League semi-final last year as well as the Serie A title.
There were emotional scenes before the match as Pioli was encircled by his players and he embraced each of them individually while the whole stadium gave him a standing ovation.
Rafael Leão immediately went over to celebrate with Pioli after scoring the opening goal in the 22nd minute following a howler by Salernitana goalkeeper Vincenzo Fiorillo, who dropped the ball at his feet.
Five minutes later it was Giroud's turn as he acrobatically struck home a corner for his 15th league goal of the season. The France forward has 49 goals for Milan in his three seasons.
Simy pulled one back for Salernitana in the 64th but Davide Calabria restored Milan's two-goal advantage 13 minutes later.
However, goals from Junior Sambia and Simy in the last three minutes rescued a draw for already-relegated Salernitana in their last top-flight match.
It was also Milan defender Simon Kjær's last match for the club. Pioli, Giroud and Kjær were all celebrated in a special ceremony after the match
RAlex Sandro made his 327th and final appearance for Juventus as the Brazilian equalled Pavel Nedved's record for the most matches by a foreign player for the Bianconeri.
Alex Sandro headed in Juve's second in a 2-0 win over Monza. Federico Chiesa claimed the opener two minutes earlier.
Nicolò Fagioli hit the crossbar in the 16th minute on his first start for Juventus since returning from a seven-month ban for betting violations.
Monza forward Alessio Zerbin was sent off in the final minute following a second yellow card.
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