Lehman has confirmed that it will acquire 100 per cent of the brokerage, although it did not say how much it was paying.
However, insider sources quoted in the media say that the deal is worth around $95 million.
The acquisition will bring Lehman its first presence in Australia, and has been seen as an attempt by the Wall Street bank to access the boom in corporate activity in the region.
Asia is currently the fastest-growing market for investment banking, and Lehman is seen to need a boost in income in order to catch up with its more profitable US rivals.
Commenting on the deal, Lehman's Asia chief executive Jesse Bhattal said that the bank intended to build Grange Securities into a significant presence in the coming months and years.
"This acquisition is about setting up a beach-head and we will play in the next five years or so a dominant role in expanding that product offering," Mr Bhattal told reporters in Sydney, according to Reuters.