The sites will be divided equally between the two partners, with 30 being retained by Morrisons. The retailer said the book value of its share in the net assets of the partnership was£67.4 million.
The transaction will be completed before the end of June. The Safeway stores on the sites that will go to BP will continue to operate until the end of the year, when they will be rebranded as BP Express. No redundancies are expected.
BP UK retail director Graham Sims said: 'The partnership was a leading-edge concept when we started and both companies have proved how successful this format can be. It has achieved all of the goals that we both wanted it to achieve, but we feel now is the time to move on.'