The deal is reportedly worth €7 million.
"Ibrahimovic rejoined his teammates and coach Stefano Pioli at Milanello Sports Center, where he took part in his first training session of the season," the club said in a statement.
The 38-year-old landed in Milan on Saturday and greeted fans at the city's Linate airport. He was due to undergo coronavirus testing before reuniting with his teammates at the club's training complex.
"As I've always said, I'm not here to be a mascot," Ibrahimovic said. "I'm here to get results and to help the team, the coach, and the club get Milan back to where it belongs."
The veteran striker rejoined AC Milan on a short-term basis in January and helped the Rossoneri finish sixth in the Serie A table with 11 goals and five assists in 20 league appearances.
He first joined the club in 2010 on an initial loan deal from Barcelona and won the Serie A title that season. Ibrahimovic scored 56 goals in 85 appearances during his first stint with Milan.
His ties to the seven-time European Cup winners remained intact even after leaving the team for Paris Saint-Germain in 2012. Ibrahimovic gave Milan credit for bringing his "smile back" after a forgettable year at Barcelona that resulted in several clashes with manager Pep Guardiola.
Ibrahimovic - who played for PSG, Manchester United, and the LA Galaxy between stints with Milan - returned to the Italian club in December, shortly after a humiliating 5-0 defeat to Atalanta left it in 11th place.
Milan went 13-6-2 with Ibrahimovic back in the squad and recorded wins against Roma, Lazio, and Juventus.