The new organisation will be known initially as St Mungo’s Broadway, but the charities said a new name and identity would be considered.
A spokesman for Broadway said the boards wanted to create an organisation of "national reach and impact that can provide a greater depth and range of services for homeless and vulnerable people". He could not give more detail on the new charity's plans.
St Mungo's services are in London and the south of England; Broadway works mainly in London but also runs an outreach scheme in Oxford. Broadway has 254 staff and St Mungo's has about 950 full-time staff.
When asked whether the merger would result in job cuts, Broadway's spokesman said the charities were "not merging to save money. However, we will need to be competitive as we tender and re-tender for services. Both boards will now work on the practicalities of merging, with the core aim of building on both charities' existing services. "
The spokesman said there would not be any changes to services or office closures as a result of the merger.
Howard Sinclair, chief executive of Broadway, will lead the new organisation and has been appointed chief executive designate. Charles Fraser, chief executive of St Mungo’s who has led the charity for nearly 20 years, announced in September that he would step down in April.
A spokeswoman for St Mungo's said she was unable say whether Fraser’s departure was linked to the merger. The merger plans have already undergone three months of due diligence.
Paul Doe, chair of St Mungo's, will become chair of the new organisation and Sir Leigh Lewis, chair of Broadway, will become vice-chair.
In their 2013 accounts, both charities commented on what a difficult year it had been.
The Broadway spokesman said: "Both Broadway and St Mungo’s are financially sound and neither organisation needs to merge. This is an opportunity to combine to better meet the increasing needs of homeless people."
St Mungo's had an income of £49.1m and reported a surplus of £1.3m in the year to March 2013. The surplus was down on the £3.4m it made a year earlier, which was "a further indication of the impact of funding cuts and our need to be competitive when tendering", the accounts said.
Broadway had an income of £15.6m in 2012/13 and reported a deficit of £255,112 over the same period, although this was more than covered by its reserves.
The cost of improving its systems to increase fundraising, and of due diligence on a merger with People Can – which it pulled out of because of the size of that charity's pension liabilities – accounted for almost three quarters of its deficit.