In December, the receiver said workers would be guaranteed employment until the end of March.
The Lindsey refinery is located next to the Phillips 66 Humber refinery.
Phillips 66 said it had agreed to buy the under-threat refinery and planned to integrate the operations into its neighbouring site.
It said it had decided not to restart standalone refinery operations at the Lindsey site because it was not “viable in current form”.
Paul Fursey, the firm’s lead executive, said: “We recognise and deeply sympathise with how difficult the closure of the site has been for the workforce and the local community.
“This sale is the best way forward to secure jobs, bolster the local economy and encourage investment in the region.”
Shanks added: “Phillips 66 is an experienced and credible operator, and today’s sale agreement allows them to quickly expand operations at its neighbouring refinery, with all remaining staff guaranteed employment until the end of March.
“This will expand the company’s ability to supply fuel to UK customers, boosting domestic energy security and securing jobs – including hundreds of new construction jobs over the next five years.”
The sale of the site is expected to be completed in the first half of 2026.