Milan, under new coach Massimiliano Allegri, have looked shot-shy in pre-season and the Rossoneri have decided to rip up their frugal recent transfer policy to land a player who dominated Serie A during his time with Juventus and Inter.
"We have agreed a deal for a season's loan and then the right to buy for 24 million euros," Milan chief executive Adriano Galliani told reporters in Barcelona.
"He will undergo a medical on Monday and sign a four-year contract."
The complex deal allows for the 28-year-old to pen a long-term deal with Milan despite no cash yet being handed over to Barcelona, effectively making the option to buy compulsory.
Galliani has brokered a cut-price deal having been locked in talks with Barca since Wednesday.
Swedish international Ibrahimovic joined Barca from Inter in July 2009 in a swap deal with Samuel Eto'o worth a total of 66 million euros but the player had a mixed first season at the Nou Camp.
His relationship with coach Pep Guardiola became strained and the recent arrival from Valencia of Spain striker David Villa threatened his place for the coming season.
Silvio Berlusconi's Milan have made a habit of signing ex-Inter players, most notably Andrea Pirlo and Ronaldo, and most Rossoneri fans do not care who arrives as long as they can challenge for a first scudetto since 2004.
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Ibrahimovic won the 2007, 2008 and 2009 Serie A titles with Inter but quit saying he had nothing left to win in Italy and craved Champions League success.
Inter triumphed in the Champions League without him last season and also scooped the scudetto and Italian Cup in an unprecedented treble.
"There's nothing to explain," Ibrahimovic told Sky Italia when asked what Inter fans might think about him joining their city rivals.
"They won everything without me. With me, we did well, we won something. But now I'm a Milan player.
"I'm very happy. Everything was resolved in a good way. Milan are one of the biggest clubs around. My dream is to win the Champions League with Milan."
Netherlands striker Klaas Jan Huntelaar was left out of Milan's squad for Sunday's Serie A season-opener at home to Lecce, suggesting he may be about to leave before the end of the transfer window on Tuesday.
"Is the trio of Ibrahimovic, Ronaldinho and Alexandre Pato the strongest in Europe? I believe it is," a beaming Allegri told a news conference.
