Waterloo Library will close in its current form in mid-July, Lambeth Council has confirmed.
Although the new library will have longer opening hours (weekdays 9am-6pm and Saturdays 9.30am-5.30pm), it will not have Lambeth libraries staff on hand at all times.
The council says libraries staff will visit Waterloo "on a daily basis".
"I'm delighted that, by working with a strong community organisation like Oasis, we are able to keep a library in Waterloo," said Cllr Jack Hopkins, Lambeth cabinet member for regeneration, business and culture.
"In the face of massive government cuts, we have worked very hard to maintain libraries in all ten existing locations across Lambeth.
"The new service in Waterloo underlines this commitment and to nourishing and serving our local communities."
Steve Chalke, founder and leader of Oasis Global, said: "We are looking forward to providing the Waterloo library with a new home and welcoming library users to the refurbished Oasis Centre.
"Oasis' goal is always to work in partnership to do all we can to help build a safe and healthy community.
"Hosting the library is one way of achieving this. The library is in a great location, easily accessible on foot or by public transport. I invite the local community to visit, read, learn and explore."
The Waterloo Job Shop will remain open at the Lower Marsh building.