The charities said the move, which was finalised on 1 September, would help both organisations expand and strengthen their work with young people, and allow UFA to expand its work.
UFA will retain its own identity and branding, and there will be no changes to the staffing structure of either charity, the organisations said.
UFA employs 70 people, but has more than 500 when its work with the National Citizen Service is taken into account. P3 has more than 700 employees.
All of UFA’s trustees have been offered a place on P3’s board, but the make-up of the new board is yet to be decided, a spokeswoman for the charities said.
UFA will also remain in its Birmingham offices, the spokeswoman confirmed.
P3 had an income of £36m in the year to 31 March 2018; UFA had an income of £5m for the same year.
The charities said the merger would help both organisations make savings that would be reinvested in their charitable work, and P3 will provide additional infrastructure support to UFA.
Mark Simms, chief executive of P3, said: "By working together we will create a stronger presence for both charities that will enable us to support more young people, earlier, our combined expertise supporting young people out of crisis situations and enabling them to access training and education.
"By sharing best practice from both organisations we’ll be able to offer a broader range of services and support more young people."
Paul Evans, chief executive of UFA, said: "By joining the P3 Group we will become a stronger organisation, better equipped to respond to the needs of young people today and better equipped to ensure we deliver the maximum impact for all the people we work with.
"I believe this partnership will enable UFA to realise its further ambitions and empower more people to achieve great things."