Home Retail Group said that it began discussions with Wesfarmers in September, with a firm offer resulting in November.
Wesfarmers owns Australia's biggest home improvement retailer, Bunnings, as well as the Coles supermarket chain.
Although the company has completed due diligence, talks were continuing.
Home Retail said that Wesfarmers was a "substantial and strong group with an ambitious plan" to develop Homebase and that the £340m cash price offered good value for shareholders.
John Walden, chief executive of Home Retail, said the sale would allow the company to focus on Argos with an improved financial position, which represented "an even greater opportunity for building long-term shareholder value".
Earlier this month, Sainsbury's said that Home Retail had rejected its bid to buy the Argos chain.
On Tuesday, the supermarket issued a 22-page presentation outlining why a takeover of the catalogue and online retailer was "strategically compelling".
Sainsbury's could close between 150 and 200 Argos stores and move them to a nearby supermarket, the BBC understands.
Many store leases are due to expire in the next couple of years and Sainsbury's has excess space in many of its stores.
Under the deal being proposed, Wesfarmers would buy the entire Homebase business, including all stores and distribution centres. Product brands such as Habitat would not be included, but licensed for use by Homebase for one year.
Shares in Home Retail, which updates the market on its Christmas trading on Thursday, closed up 4.1% at 147.7p before the Homebase announcement.
The stock has jumped by more than 50% since Home Retail's rejection of the Sainsbury's bid was revealed.
The owner of Homebase has said it is in advanced talks to sell the DIY chain to an Australian retailer, Wesfarmers, for £340m.