The 25-year-old has signed a contract until June 30, 2031, which a source said is worth 74 million euros, rising to 90 million euros with bonuses, a club record.
"AC Milan welcomes Goncalo Ramos and wishes him every success with the Rossoneri," the Italian club, which finished fifth in Serie A last season, said in a statement.
Ramos is at the World Cup with Portugal and will play under fellow countryman and new Milan coach Ruben Amorim.
Milan's previous record signing was Ramos' compatriot Rafael Leao, who joined Milan from Lille for 49.5 million euros in 2019, according to expert website Transfermarkt.
Cristiano Ronaldo's 117-million-euro move from Real Madrid to Juventus in 2018 is the overall record, for any position, in Serie A.
"Today, one of the most defining chapters of my career is coming to an end," Ramos said on Instagram.
"Wearing the PSG shirt has been a privilege and an honour I will carry with me forever.
"I'm leaving, but I'm leaving a part of my heart in this club.
"PSG will always be a home for me, and I will always be proud to have helped write a chapter of its history," he added.
Ramos has spent three years at French champions PSG, winning the Champions League twice, after his 65-million-euro arrival from Benfica.
However, he has struggled to hold down a regular first-team place, playing second fiddle first to Kylian Mbappe and then Ousmane Dembele as PSG's centre-forward.
Ramos did not start a single Champions League match for PSG this season.
He scored 45 goals for PSG in his three seasons, in 131 matches, many of which as a substitute.
Ramos won three Ligue 1 titles, having also won the Portuguese league with Benfica, and two French Cups.
"Paris Saint-Germain thanks Goncalo Ramos for his professionalism, commitment, and contribution to the club's many successes, and wishes him the best for the remainder of his career," the French club said in a statement.