Plans to create a Care Leaver Covenant were first announced in May 2016 as a way to encourage organisations to offer more support to care leavers in England. It was due to launch in October 2016 but has suffered a series of delays.
Speaking at the ADCS conference in Manchester, Zahawi said he wants local councils, the school system, the health service, the local leisure centre and companies, and government departments to be catering for their needs.
He said the DfE had been "leading the way" in Whitehall, setting aside roles for care leavers in its civil service internships scheme.
"[But] there is a limit to how much we can offer alone," Zahawi said.
"That is why I am so excited to be launching the Care Leaver Covenant this autumn, and I'm standing on the shoulders of giants by bringing [former children's minister] Edward Timpson's idea to life.
"The covenant is a pledge from organisations across our society, in which they make concrete commitments to help improve outcomes for care leavers. They might offer training, job opportunities, services or anything else they can offer to help young people move from care to independence.
"It represents a partnership between the best of the public and private sectors to provide support that will champion our most vulnerable children.
"And my ask of all of you today is to do all you can to encourage your local businesses to be ambitious in what they can offer to support our future generations."
Zahawi also used his speech to note concerns from directors of children's services about pressure on budgets in the face of rising demand, an issue touched on by ADCS Stuart Gallimore during his own speech.
"I should also say that I have heard a clear message, which I've heard again today, that funding is a real challenge," he said.
"I want to acknowledge this, and say that I am listening - and I particularly want to work with you to understand the evidence for additional investment."
Zahawi also praised progress made by the sector in recent years towards creating the "best system possible".
"Since 2016 you have been making real strides towards this goal, implementing the reforms set out by my predecessor Edward Timpson in Putting Children First," he said.
"I am a big supporter of this strategy - I believe we are building an infrastructure that has the potential to be truly transformational. And I see my job now as one of implementation: helping to oversee this transformation but, more importantly, ensuring no barriers get in your way."