Work will start before winter on turning Walkley Library into a shared venue featuring a café bar.
Councillors have granted True North Brew Co planning permission for the project.
The firm has bought the Grade II listed building on South Road and will lease an area back to the council to be run by volunteers as a library.
True North will repair the building, create a mezzanine floor inside and add an extension with kitchens, offices, toilets and a cellar.
The company has also promised to raise £6,000 per year towards library services.
Work to renovate the windows and improve disabled access will start this year, with the extension and café bar set to open in 2017.
A spokesman said: “True North Brew Co hope Walkley library will become a cultural, community hub. A place for parents and their children, local community groups and students alike to use, creating a lively and enjoyable environment whilst enjoying great local beers, food and coffee.”
Full and part-time jobs will be created by the scheme.
The spokesman added: “The renovation and extension of Walkley Library will bring a number of full and part-time jobs to the area.
“True North have agreed to manage and maintain the library building for 21 years. This is a large commitment for an independent business, taken on due to the significance and importance the company believes a library has within the community.”