Wandsworth is one of just seven local authorities taking part in a pilot scheme to end child poverty.
For the next two years, teenage parents will receive training in life skills to help them take better care of their children.
The Improved Housing Support for Teenage Parents Scheme is sponsored by a new Government grant.
Councillor Kathy Tracey, executive member for children and young people, said: "The objective is to enable teenage parents to have the opportunity to live independent and successful lives, to provide loving and stable homes for their children and to prove that with the right support, teenage parents can turn around their lives and provide a better start for their children than they perhaps experienced themselves."
The scheme also aims to reduce teenage pregnancy levels and reduce youth homelessness.
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