A statement issued by the charity said that, in the face of "significant changes and prevailing economic conditions", it has "not been possible to sustain the organisation".
Some of the organisation's functions will transfer to children's charity Coram, resulting in the creation of a new entity, CoramBAAF Adoption & Fostering Academy.
CoramBAAF will continue to operate as a membership organisation for agencies and individuals in the UK, and will take on Baaf's work on research, policy and development, professional advice and professional development; publications; the National Adoption Register for England, the Independent Review Mechanism; National Adoption Week, and adoption activity days.
BAAF Scotland, BAAF Northern Ireland and BAAF Wales will continue to trade for a brief period while options to transfer some of their services and staff to an alternative provider are considered.
"This has been a difficult decision for the board," a statement from Baaf said.
"We appreciate that this is a very challenging time for our dedicated staff and are committed to giving them as much support as is possible during this period.
Dr Carol Homden, chief executive of Coram, said: “Coram is the oldest children’s charity and has been delivering fostering and adoption services for 275 years.
"The CoramBAAF Adoption & Fostering Academy is a sustainable way forward which enables the expertise of two organisations renowned for their work with looked after children to be shared to create better chances for children.”