Industry sources suggested the purchase price of Sydney-based Custom Coaches was in the region of £20 million to £25m.
The acquisition of Custom, which employs 400 people at manufacturing sites in Sydney and Adelaide, will add new products to the Scottish bus-builder's portfolio, such as heavyweight single deckers and articulated vehicles.
Custom has annual sales of about £55m and a 24% share of the bus market in Australia.
Alexander Dennis, which employs 900 people at its headquarters in Falkirk and builds around 2000 buses a year, said this was the first outright acquisition it had made since being rescued from administration eight years ago.
Group corporate affairs director Bill Simpson said: "This is good news for the workforce in Falkirk.
"There is an expertise there in kitting, putting boxes of 3000 parts together, which will be crucial. The engineering experience we have there will also be of value as we move into this new market.
"We believe we have a great range of products which we can take to other parts of the world."
Turnover for 2012 is expected to be more than £430m with the acquisition of Custom expected to push sales towards £500m.
Chief executive Colin Robertson said: "This is another significant step in our strategy to diversify and grow the business.
"The Custom brand is an icon in the Australian bus-body market, having been part of the transport landscape for 50 years. It has history, heritage and a reputation for quality products and putting customers first.
"These are the fundamentals of our business philosophy at ADL, and we will build on them as we bid to turn a successful brand into a great Australian business.
"Our strategy will be to invest in people, processes and products; to exploit the synergies between our companies, particularly in terms of product and technology transfer."
Alexander Dennis already has a manufacturing partnership in New Zealand with Kiwi Bus and sites in China, with the move into Australia seen as the next step in opening up the Asia Pacific region.
Mark Burgess, managing director of Custom, said: "There are clear synergies between the two companies.
"Bringing these strengths together presents the opportunity to create a powerful new force in the Australian bus-manufacturing sector."
The deal comes just a few weeks after Alexander Dennis announced a strategic alliance with Canadian business New Flyer Industries Inc to expand its presence in North America.
It believes there is annual demand for around 1000 lightweight, fuel-efficient buses to meet demand from operators across the United States and Canada.
Alexander Dennis was rescued in 2004 by a consortium of Scottish business people after its parent company Mayflower Corporation went into administration.
Sir Brian Souter, Ann Gloag, Sir David Murray's Murray Capital and Noble Grossart Investments plus Mr Robertson are the current shareholders in the business, according to its annual return filed at Companies House.