But even so, the island still faces huge logistical hurdles to distribute badly needed food, fuel and drinking water.
More than a quarter of all pharmaceutical drugs exported from the USA are made in Puerto Rico.
But Maria knocked out the United States territory's entire power grid, crippling its water and sewage treatment system.
Scott said the Puerto Rican leaders identified the need for supplies to be quickly shipped to the island.
He tweeted that relief supplies are getting through. Diesel fuel, which is desperately needed to run generators for emergency services such as hospitals, is scarce. We welcome more help.
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Media captionUS Navy evacuates residents from storm-devastated Dominica How is the US responding?
But the transport of relief supplies has been hampered by roads rendered impassable by fallen trees or flooding.
Trump told reporters on Wednesday that "we're thinking" about lifting the law, but added that a "lot of shippers" didn't want it lifted.
President Trump was criticised for spending the weekend focusing on a feud with National Football League players and coaches, instead of the Puerto Rico disaster. "One is to land in San Juan and pay tariffs associated with the Jones Act, or to take shipments to Jacksonville, offload the ship and reload it on a USA one".
By waiving the Jones Act, the USA will allow for more rapid delivery of aid to Puerto Rico.
The Jones Act limits shipping between coasts to US -flagged vessels.
The regulation was created to promote the American commercial shipping industry. Puerto Rico, for example, has no voting power in Congress.
This means aid from countries such as the nearby Dominican Republic can not directly be sent to the devastated island.
Shortly before meeting Trump Thursday, Acting Department of Homeland Security Secretary Elaine Duke issued a statement saying, "This waiver will ensure that over the next ten days, all options are available to move and distribute goods to the people of Puerto Rico".