The project by the University of York will see Sanderson House on the Chapelfields estate used as a community space.
Study and play activities would be offered as well as support for adults in the community, officials said.
Councillor Michael Pavlovic said the centre would "help improve educational and social outcomes in the area".
Mr Pavlovic, executive member for communities at City of York Council, said the centre would provide more opportunities "for people to come together in the Chapelfields and Westfield area".
The council has agreed to lease Sanderson House for a five-year period.
University of York Vice-Chancellor, Professor Charlie Jeffery, said staff had met with several schools in the area to "understand the challenges they face".
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