It is the first time the regulator has reached an agreement with an individual local authority since its Young Adults Advisory Group began funding training courses last year.
Staff working in both the youth service and social services departments will be given the chance to attend a series of free training days between now and Christmas. They will then be expected to run sessions with young people on the margins of society about how to handle their money and avoid getting into debt.
The advisory group is also in discussions with voluntary sector providers in Southwark about sending staff to the courses. A range of organisations, including accommodation provider Centrepoint and environmental charity Groundwork UK, have agreed to attend so far but the FSA is hoping to attract more in the coming weeks.
The FSA, which set itself the target of training up to 20,000 youth professionals by the end of 2010, estimates that one in five 22- to 24-year-olds have debts of more than £5,000.
Linda Jack, youth adviser at the FSA, said: "We looked at a range of local authorities to pilot the scheme before deciding on Southwark. The borough has a reasonably high number of young adults not in education, training or employment and is a manageable size. There was also the political will on a local level to make this happen."
An evaluation of the impact the training has had on young people will be carried out in the New Year. The courses will then be revised based on the findings before being expanded to other boroughs from early next year.
Last week, the FSA signed deals with Citizen's Advice Northern Ireland, Fairbridge, Lifeline and A4E to deliver its courses throughout the UK.