The sale of 12 C-130 J Super Hercules transports and accompanying equipment is worth $2.2 billion.
The US Defense Security Cooperation Agency said the sale, still not finalized, "will improve Egypt's capability to meet current and future threats by providing airlift support for its forces by moving supplies, equipment, and people," AFP reported.
The aircraft can also be used for maritime patrol and rescue missions, it added.
In a second deal, Egypt can buy ground-based air defense systems worth $355 million to help it fend off air threats.
The deals come despite ongoing unease in Washington over Egyptian President Abdel Fattah al-Sisi's tough treatment of political opponents, with rights groups estimating that Egypt holds about 60,000 political prisoners.
In September, the State Department put a hold on $130 million in military aid already budgeted for Egypt because of lack of improvement in the human rights situation in the country.
And in early November, Secretary of State Antony Blinken urged Egypt in bilateral talks to make "tangible and lasting improvements" on human rights.
But for fiscal year 2022, which began on October 1, 2021, the Biden administration budgeted $1.4 billion in bilateral assistance -- most of it military related -- for Cairo, the same as the previous year.
Two lawmakers who have been critical of US arms sales to Egypt said Tuesday that Egypt has not met the conditions required to remove the suspension on the frozen $130 million.
"We welcome the recent release of several high-profile Egyptian political prisoners," said Don Beyer and Tom Malinowski, co-chairs of Congress' Egypt Human Rights Caucus.
However, they said it was not enough and urged Biden to keep the freeze on the aid.
"Tens of thousands of political prisoners... remain in Egyptian prisons," they said in a statement.
"The government of Egypt has continued to engage in widespread torture, suppression of dissent, and even persecution of American citizens and the families of critics living in the United States," they added.
The two arms deals also gained approval nearly three weeks after US authorities arrested a New York man accused of spying on political opponents of Sisi.