They have become the latest Middle Eastern airlines to let passengers take laptops in the cabin on US-bound flights.
Both carriers said they had worked with US officials to tighten security checks on flights from Kuwait and Jordan.
The ban was imposed in March on direct flights to the US from eight mainly Muslim countries to address fears that bombs could be concealed in the devices.
Etihad, Turkish Airlines, Emirates and Qatar Airways became exempt last week.
Royal Jordanian, which flies to three US cities from Amman lifted the ban after new security measures were implemented for US-bound flights, airline president Stefan Pichler said.
State-owned Kuwait Airways, which flies from Kuwait to New York via Ireland, said the ban was lifted after US officials inspected security measures on its flights.
Last month, the US Department of Homeland Security announced measures requiring additional time to screen passengers and electronic devices on US-bound flights from 105 countries.
Airlines expressed hopes at the time that the changes would pave the way for the lifting of the electronics ban.
The Morocco, Egypt and Saudi Arabia airlines are yet to announce a lifting of the ban.
Saudia, the flagship carrier for Saudi Arabia, has said passengers would be able to take personal electronic devices on US flights from July 19.
Royal Air Maroc also believes it can have the ban lifted for flights out of Casablanca by the same date, a senior official told Reuters last week.
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