The Milford Haven refinery, which employs about 400 people, has been up put up for sale for more than three years.
Preseli Pembrokeshire Member of Parliament Stephen Crabb told Western Telegraph that the agreement in principle signed by Murphy with the buyer is a hugely positive step forward.
"I am delighted with the breakthrough today in negotiations over the sale of the Murco oil refinery in Milford Haven," Crabb added.
"The sale will secure hundreds of high quality jobs and will enable the refinery to continue operating fully."
"There remain challenges ahead, and a due diligence process to be completed, but I am just so pleased that we have reached this point. I am very optimistic that the sale can be completed."
Capable of producing 135,000 barrels of oil a day, the 41 year-old refinery plant is recycling oil products currently to keep itself operational, according to Telegraph.co.uk.
Energy Global? cited a Welsh government spokesperson as saying, "The plant is a vital part of the Welsh economy and we have been working tirelessly to secure its future, working closely with the current owners, potential buyers and government at all levels."
