Hayward has helped to set up Vallares, which on Thursday said it plans to raise £1.0 billion (1.13 billion euros, $1.64 billion) via a stock market flotation in London later this month.
Vallares said in a statement that it "intends to acquire or establish a major company, business or asset that has significant operations in the resources sector, with a focus on the oil and gas industry."
Hayward said: "We will have the cash, access to funds and the capability to unlock value where the current owners have neither the capital nor technical expertise to develop assets."
Hayward resigned as chief executive of BP last July after being vilified in the United States for his handling of the environmental catastrophe along the Gulf of Mexico coast.
He was heavily criticised over his gaffe-filled handling of the disaster, especially after saying that he wanted his "life back" and downplaying the environmental impact of the spill.
An explosion on the BP-leased Deepwater Horizon rig in the US Gulf of Mexico in April 2010 killed 11 workers, caused millions of barrels of oil to spew into the sea and left the British company scrambling to meet huge compensation costs.