Among the 15 farms are Tillington Fruit Farm in Herefordshire, which grows substantial volumes of apples as well as other fruit, Rosemount in Perthshire, which focuses on soft fruit, and its field vegetable growing Coldham Estate in Cambridgeshire.
The trust's chief investment officer Danny Truell said: "The Wellcome Trust has a strong track record as a long-term investor which values responsible stewardship over quick profits.
"We believe that we are ideally placed to develop and grow the Co-operative Group’s farms and farm business while providing continuity."
Among the service which the trust will maintain is the Co-operative’s Farm to Fork education programme.
The Co-operative Group's interim chief executive Richard Pennycook said: "In the Wellcome Trust we have a buyer whose values are closely aligned to those of The Co-operative.
"The Wellcome Trust has acquired an excellent farming business characterised by the quality and professionalism of colleagues and high levels of customer service. I expect the farming business to continue to thrive under their committed long-term ownership."
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