A multi-million-dollar technology for Riyadh was blocked by the former president during the final months of his administration over human rights concerns.
Saudi Arabia is leading a military coalition targeting Yemen with air strikes.
By approving the measure, Secretary of State Rex Tillerson may have given an indication the Trump administration will seek closer ties with Saudi Arabia in the Yemen war.
Officials say the deal will need White House approval to go into effect.
Last year, Obama's administration approved a $1.15 billion deal for the sale of tanks and armored vehicles to Saudi Arabia, according to The Independent.
The deal was opposed by more than 60 members of the House of Representatives, who signed a letter calling for Obama to delay.
However, in his final months in office, Obama decided to halt the current deal on precision-guided military technology.
At least 10,000 people have been killed in the fighting in Yemen that has unleashed a humanitarian crisis on the impoverished country.
If the White House agrees with the State Department's position, the administration would notify Congress about the intended sale, where it could encounter resistance.