0833 GMT April 03, 2020
The 38-year-old signed a six-month deal with the Serie A side, with the option for another season, BBC Sport reported.
The former Sweden, PSG, Inter and Manchester United striker scored 42 goals in 61 league games in his previous stint at the club from 2010 to 2012.
"I know what I have to do. Zlatan is still here," he said on Friday.
Ibrahimovic, who was a free agent after leaving Major League Soccer side LA Galaxy in November, said he received "more offers at 38 than when I was 20".
"I've been looking for one final rush of adrenaline to give it my all," he said as he marked his return to the Rossoneri.
"I received even more calls after the game against Atalanta [which Milan lost 5-0].
"I didn't come here to be a Rossoneri mascot. I've never lost my passion."
AC Milan is 11th in Serie A, with 21 points from 17 games.
The seven-time European champion is without a major trophy since its 18th Italian title in 2011.
Ibrahimovic added that a "corporate decision" led to his departure from the club in 2012.
"The last time I left, it was without my approval but the situation was what it was," Ibrahimovic added.
"What's important is that I'm here and I want to improve things as much as possible."
AC Milan's next Serie A game takes place on Monday against Sampdoria.