The gallery will be built by investment manager and art lover Jonathan Ruffer, who owns nearby Auckland Castle.
He hopes some paintings will come on loan from the Museo Nacional del Prado in Madrid, Spain’s national gallery.
In 2012, Mr Ruffer paid £15m to keep a collection of 17th Century Spanish paintings in the UK.
The 12 paintings by Francisco de Zurbaran hang in Auckland Castle, the former home of the bishops of Durham. Mr Ruffer bought the castle itself as part of the deal.
He is now setting about making the region a centre of excellence for classical Spanish art.
The £4m gallery will open in the former branch of Barclays bank in the town’s market place in early 2017.
“The central element of it will be 17th Century golden age Spanish paintings, but we will have Spanish paintings from other periods,” Mr Ruffer said.
Great Spanish art, he said, was “very powerful” and “timeless”.
The town will also get a new art research institute as part of Durham University. The Bowes Museum, 15 miles (24km) away, already has a world-class collection of Spanish paintings.
“I want to see this area regenerated and the key to doing that is to bring people to this part of the world, and that’s done by building on what’s already here,” Mr Ruffer said.
“The local tradition of Spanish pictures, which is largely the coming together of separate coincidences, is one that can be built on.”
Loans from international collections will be “an important part of what we do”, he added.
The Prado has an “amazing number of absolutely first-class stuff in reserve”, Mr Ruffer said.
“Particularly very big pictures, because the Spanish painted big pictures, and no gallery has the capacity to hang dozens of these things. But here we could hang them.”
The Prado has the largest collection of paintings by great Spanish artists like El Greco, Velazquez, Goya, Ribera and Zurbaran.
Prado curators are currently in the region to look at the site of the new gallery and take part in a conference on Spanish art.
As well as the gallery and research institute, Mr Ruffer is planning a new £17m wing on Auckland Castle to house a museum tracing 5,000 years of religion, which will open in 2018.