The 38-year-old was a free agent after leaving Major League Soccer side Los Angeles Galaxy at the end of his contract in early December.
In his previous stint with the Rossoneri between 2010 and 2012, Ibrahimovic scored 56 goals in 85 games and helped them to their last Serie A title in 2011.
Milan said on their club website: 'AC Milan is delighted to announce the signing of Zlatan Ibrahimovic.
'The club and the striker have agreed on a deal until the end of the current season with an option to extend the contract for the next one.
'The deal is subject to medical and all regulatory processes. Ibrahimovic will be in Milan on January 2, 2020 to take his medical and he will then join his teammates for his first training session.'
AC Milan have had a wretched start to the season as they lie 11th on the Serie A table.
The seven-time European champions have already made one managerial alteration this season, but replacing Marco Giampaolo with Stefano Pioli has failed to galvanise the side.
Last week, they lost 5-0 to Atalanta, which was their biggest defeat for 21 years.
"I'm coming back to a club I hugely respect and to the city of Milan I love," Ibrahimovic told Milan's website.
"I'll fight together with my team-mates to change the course of this season. I will do everything to make it happen."
