The Savers Support Fund will support money management projects that work with young people aged between 14 and 25 or families considered to be "just about managing".
The second fund, called the Early Years Social Action Fund, will help to grow initiatives that support the parents of children aged four or less.
Both funds will offer four to six grants of between £150,000 and £250,000 to the successful projects.
Last year four funds, worth a combined £4.9m, were launched by the Office for Civil Society and Nesta.
Those four funds included three focused on volunteering among the over-50s and one on increasing digital volunteering in schools.
Vicki Sellick, director of Nesta, said: "We’re delighted to launch two new funds to mobilise thousands more volunteers to give their time alongside schools, councils and other public services. The innovations we back to grow through these new funds will make a lasting difference in improving the chances of pre-schoolers in succeeding and in helping young people and adults in debt to learn life-long habits of saving and money management."
Rob Wilson, the Minister for Civil Society, said: "Volunteers are invaluable, supporting communities and helping to build a shared society for everyone. These latest funds will increase the numbers of volunteers even further, supporting more parents and helping adults and young people develop a positive relationship with managing money."