The government and the UN agencies said in a joint statement that the initiative would aim to reach 166,667 Lebanese and 200,000 non-Lebanese vulnerable children for the 2015-2016 academic year.
"Our responsibility is to ensure that every child on Lebanese territory has access to education," said Education Minister Elias Bou Saab.
Lebanon, a country of four million people, hosts more than 1.1 million Syrian refugees, including at least 400,000 school-aged children, according to the UN's refugee agency, UNHCR.
The $94 million project would cover the costs of school registration, supplies, and parental funds for refugees as well as vulnerable Lebanese children up to grade nine.
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A similar programme last year provided free education and supplies for 100,000 Syrian children.
"This year marks a major breakthrough: we will double the number of children enrolled in Lebanese public schools compared to last year," said Tanya Chapuisat, UNICEF's Lebanon representative.
"However, with all the efforts expended, at least 200,000 refugee children still remain outside of the formal education system, deprived of their basic right."
UNHCR representative Mireille Girard said the agency's "priority is to identify out-of-school children and encourage their integration in Lebanese public schools."
"At a time when refugees are facing increasing challenges in their daily lives, certified education for their children is much needed."
According to UNICEF, more than 2.6 million children from war-ravaged Syria are out of school, sparking fears of a "lost generation."