Can will remain a registered charity and limited company in its own right under the new arrangement, which took effect on 1 October.
A Richmond Fellowship spokeswoman said Can would continue to have its own chief executive and board. No redundancies are planned.
Richmond Fellowship, which has 886 staff and an annual turnover of £33.4m, offers a range of housing, care, employment and community support for people with mental health problems.
Can, which provides drug, alcohol and homelessness services to people in Northamptonshire and Bedfordshire, has 120 staff and an annual turnover of £6.7m.
Derek Caren, chief executive of Richmond Fellowship, said in a statement: "We believe that joining up with other ambitious and successful organisations will allow us to offer a wider range of services, develop more innovative ways of providing support and reduce our costs.
"Can has been providing high-quality support for more than 40 years and brings with it a lot of expertise in the field of substance misuse services that will benefit the rest of our organisation."
A statement from Linda Juland, chief executive of Can, said: "We’re really pleased to be joining up with the Richmond Fellowship. We believe it shares our ambitions and values and its services provide a complementary fit to enhance the support we already offer."