The agreed share and cash offer, including Aus$1 billion (£426.3 million) of net debt, is the final stage in what was an extended battle for the country's second-largest retailer.
Last week, a private equity consortium led by Texas Pacific Group (TPG) pulled out of the running. However, Coles said the TPG buy-out group, which also included private equity firms Carlyle and Blackstone, may be interested in an alternative investment structure, but did not give details.
Reports in Australia's local press said Wesfarmers intends to retain and expand all of Coles' businesses, with plans to invest about Aus$3 billion (£1.28 billion) over the next three years.
Wesfarmers has control of more than 3,000 retail sites and employs more than 165,000 people.