The export bar was placed on the painting in November after it was sold from a privately-owned collection in Penrhyn Castle.
“The art historical significance of this unusual subject is considerable; indeed there is nothing like it in any other UK collection. It's a great coup for The Bowes Museum,” said Art Fund director Stephen Deurchar.
Money from the Art Fund and Heritage Lottery Fund (HLF) as well as from private donors helped the museum in Durham secure the 15th century painting, St Luke Drawing the Virgin and Child, at a total of £2,290,650.
It was one of two paintings sold from the Penrhyn Castle collection last year. The other, Rembrandt's Portrait of Catrina Hooghsaet, was sold at auction by Sotheby's, but was also export-barred.
St Luke will be loaned to York Art Gallery and Bristol Museum & Art Gallery following its acquisition by The Bowes Museum. Other plans for the painting include a scientific investigation and conservation project led the National Gallery.
“We are thrilled to be welcoming Bouts’ St Luke Drawing the Virgin and Child to Bristol in 2018. High profile loans of this nature help us to reinvigorate our galleries and provide our visitors with magnificent new art to enjoy,” said Laura Pye, head of culture at Bristol City Council.
The loaning schedule marks the initiation of a new partnership between the three museums.
The painting is valued for its association with Bouts, one of the leading Netherlandish painters of the 15th century, as well as the quality and subject matter of the composition.