The German-American investor, along with business partner Martin Franklin, is offering shares in the vehicle called Justice at a fixed price of £10 each, sources said.
The fund, to be chaired by former UK financial services minister and fund manager Paul Myners, will be used to make an acquisition worth £1bn to £5bn, although no specific sector or location have been identified.
US economist Nouriel Roubini, known as Dr Doom for predicting the credit crisis, is also set to be a board member.
Justice will be the third investment vehicle set up by Berggruen, dubbed the homeless billionaire for living in hotels.
His first, Freedom Acquisitions, bought a stake in hedge fund group GLG Partners, while his second, Liberty Acquisitions, bought insurer Pearl – now known as Phoenix – and last year paid $900m (£558m) for a majority stake in Spanish media group Prisa, owner of daily newspaper El Pais.
Berggruen, the son of German art collector Heinz Berggruen, last year bought German department store chain Karstadt.
Order books on the Justice offering, which has been marketed to investors in the United States, Europe and the Middle East, are expected to close within the next week, the sources said, with the shares set to begin trading next week.
The listing is being run by Citigroup and Barclays Capital.