The bid is around 10% more than Barrick originally said it would offer and follows two months of wrangling between the companies.
Terms are 0.168 of a Barrick share for each one in Acacia, which compares to the original approach of 0.153-to-one.
Acacia's exploration assets are also to be sold with any substantial gains distributed to shareholders.
Barrick is negotiating with the Tanzanian government to settle a dispute that has seen Acacia banned from exporting gold and copper concentrates since 2017.
Acacia has not been a party to those discussions.
Barrick, meanwhile, had been criticised by a number of institutional shareholders over the perceived low price of its initial approach.
The Canadian giant already owns almost two-thirds of Acacia.
At the new offer price, the outstanding minority shares are valued at £343mln and the miner in total at £951 mln.
Acacia has three producing mines in Tanzania - North Mara, Bulyanhulu and Buzwagi.