The organisations have announced that the move will take place in January, with the transfer of staff taking place on 1 June.
Simon Antrobus, chief executive of Addaction, and Ryan Campbell, chief executive of KCA, will lead the process together, the charities said.
Antrobus will remain chief executive of Addaction and Campbell will continue as the head of the KCA portion of the organisation for the "foreseeable future", an Addaction spokesman said.
The new organisation will continue to be called Addaction and its central office will remain in London.
Addaction employs about 1,200 people and had an income of £51m in 2012/13. KCA has 400 employees and an income of £25.5m over the same period.
The Addaction spokesman said that no redundancies had been identified at present but "there will be a due process and full consultation exercise over the coming months". The existing Addaction board will be interviewing for up to three additional positions, drawn from KCA’s trustees.
An Addaction spokesman said that the move came about because the two organisations were "a great fit in terms of culture, values and ambition". He said: "We believe that together we’ll be able to provide radically better outcomes for our service users and act as a stronger national voice on their behalf."
Antrobus said: "I am delighted to be able to announce our new shared direction. Recovery and a focus on exceptional service delivery is our common goal, with service users at the heart of both charities."
Campbell said: "We have worked closely to ensure that we are a great cultural and operational fit, with exciting new areas of expertise coming together that will further our ambition of treating the whole person, not just the problem they present with."
It is hoped that the move will lead to greater opportunities for staff, including more diverse career pathways, training, development and improved clinical career choices, the charities said in a statement.