London-based GSK, which sold its cancer drugs business to Swiss drugmaker Novartis in April, is expected to announce the deal on Monday, according to an FT report.
The newspaper said that GSK would pay Adaptimmune as much as $350 million over the next seven years, subject to development milestones being met.
Further payments would be due in subsequent years if GSK exercises all its options and targets continue to be met. In addition, Adaptimmune would receive sales royalties on any products that reach market, the financial daily reported.
The newspaper said GSK would develop cell-based cancer therapies that involve re-engineering patients' white blood cells to improve the body's ability to fight tumors.
The FT quoted James Noble, chief executive of Adaptimmune, as saying that the development work would be done at the company's laboratories in Oxfordshire boosting efforts to promote the so-called "golden triangle" around Oxford, Cambridge and London as a globally competitive biotech hub.
GSK and Adaptimmune could not be reached outside of normal business hours.