The merger was formerly announced at a House of Commons reception last week, although it was officially completed in September.
The Amber Trust, a 40-year-old mental health services charity based in Derbyshire, has been working with P3 since 2002.
The charities entered into a more formal collaboration three years ago through the iDecide service, which is a partnership to deliver supported housing services for Derbyshire County Council.
Both charities wanted to formalise these working arrangements through a merger, a P3 spokesman said, which has resulted in the Amber Trust becoming part of the P3 group.
The agreement will enable the two charities to share back-room costs and allow them to spend more on front-line services, he said.
But both organisations will retain their independence and operate as separate entities, he said.
The spokesman said that P3 would benefit from the Amber Trust’s established name and expertise in mental health services, while the Amber Trust could proactively seek bigger contracts and expand beyond Derbyshire.
There will be no job losses or changes to internal structures as a result of the move, the P3 spokesman said.
According to the Charity Commission’s online database, the Amber Valley Association for Mental Health Ltd, which is the trading name for the Amber Trust, had an income and expenditure of about £1.5m in the year to 31 March 2014.
It has 23 staff, compared with almost 600 at P3.
P3, trading as People, Potential, Possibilities, has grown its income from £7.8m in the year to the end of March 2011 to more than £13m three years later.
A spokeswoman for the Amber Trust said that the charity had recently been subject to proposed and actual cuts in funding and a change in service provider.
Kathy Kozlowski, chief executive of the Amber Trust, who has become a chief executive director covering mental health services at the P3 group, said: "We have been providing support for the last 40 years. However, it’s been a difficult climate over the past couple of years for any business to operate in – the charity sector has been no different.
"I’m proud of the work we do at Amber Trust supporting the mental wellbeing of people around Derbyshire. This exciting merger with P3 gives us the opportunity to bring down costs and compete for funding, which I’m certain will secure the future of this well-regarded charity for another 40 years to come."
Mark Simms, chief executive of P3, said: "This merger will further build on our already successful delivery of mental health services around the country, enabling us to continue to expand our reach and help more people in need of support. I’m excited that Amber Trust has become part of the P3 group and know that we have an exciting future ahead of us."