Speaking in a House of Commons debate on the issue, Goodwill said that the government has started drawing up plans to ensure children in foster care are eligible for the extended free entitlement, which was introduced in September.
Under the current policy, 30 hours of free childcare is available for parents of three and-four-year-olds if both work more than 16 hours per week and earn less than £100,000 a year.
Earlier this month, Goodwill said that foster children are entitled to only 15 hours, whether their carers are in work or not, affecting more than 3,000 foster children.
But he told MPs yesterday that this stance will be reversed and the government has already started working with councils and The Fostering Network on details of extending the 30 hours eligibility to carers.
Further discussions are set to take place involving foster carers and other fostering organisations next month and Goodwill hopes carers will be eligible to the 30 hours offer from September 2018.
"Since the current exclusion from the 30-hours policy for children in foster care was brought to my attention, I have been looking at it carefully," said Goodwill.
"I have instructed my officials to work up plans to allow children in foster care to take up the additional hours when it is right for the child to do so.
"We will work with local authorities, fostering service providers and others in the sector to ensure we implement this change in a way that promotes the best interests of the child. I will set out more detail about how we will deliver that shortly."
The decision has been welcomed by early years and fostering organisations.
"We have always said that all children, regardless of background, should get the best possible start in life and so we warmly welcome the government's decision to allow foster children to benefit from the 30 hours policy," Pre-school Learning Alliance chief executive Neil Leitch said.
"All too often, discussions around the 30 hours are fixated on the back-to-work agenda with little consideration given to the impact of policy decisions on the child, and so today's decision marks a welcome change of focus."
National Day Nurseries Association chief executive Purnima Tanuku also welcomed the move, but called for assurances that it is properly funded to ensure providers do not end up meeting the cost.
"Extending the scheme, however welcome, needs to be thoroughly costed with meaningful investment put in to at least cover providers' costs," she said.
"The government cannot just rely on the goodwill of nurseries and parents to pay for the shortfall in funding."
A Fostering Network spokeswoman added: "We're delighted that the children's minister has announced that fostered children will be able to access the 15 additional hours free childcare following our campaign backed by our members, MPs and other organisations.
"It is vital that fostered children are not discriminated against and the reversal of this decision will ensure that, for this particular issue, they are being treated in the same way as their peers."
Last week, Secretary of State for Education Justine Greening indicated that the government was considering a U-turn on extending the 30 hours offer to foster carers.
Critics of excluding foster carers from the extended childcare offer include education select committee chair Robert Halfon, who told CYP Now that the policy was "immoral and indefensible".