Touchdown! The two side boosters successfully landed at SpaceX's Landing Zones 1 and 2 at Cape Canaveral Air Force Station in Florida.
Musk also indicated that the hardware appeared to be undamaged and will be used again later this year to launch some of SpaceX's Starlink global broadband satellites.
"The Falcons have landed", Mr Musk wrote on Twitter, inaugurating the first successful recovery of all three rocket boosters, which will be refurbished and will re-fly in another Falcon Heavy mission this summer to carry military and science satellites for the USA air force.
While Mr. Steven was not in a position to catch the fairings from this launch, it was recently given a bigger net and is expected to be on hand in the future to make all parts of the Falcon Heavy recoverable and reusable.
SpaceX's Crew Dragon capsule, atop a Falcon 9 rocket, cleared its first unmanned test flight in March ahead of its crewed mission planned for July, while the first unmanned test for Boeing's Starliner capsule is slated for August on ULA's Atlas 5 rocket.
SpaceX tries to re-use rockets, payload fairings, boosters and other parts to try to cut down on the cost of each rocket mission.
More than a year later, SpaceX has now launched the 70-meter-high Falcon Heavy, created to carry more than 64 metric tonnes of cargo, with the Arabsat-6A on board.
The center core of SpaceX's second Falcon Heavy rocket sits atop the drone ship Of Course I Still Love You.
NASA announced that this will be SpaceX's 17th Commercial Resupply Services contract mission to the International Space Station.
It consists of the equivalent of three Falcon 9 rockets combined, tripling its thrust.
The payload fairings are clam shell-like nose cone halves that protect the craft's payload.
Falcon Heavy lifted off yesterday from Cape Canaveral in Florida and successfully delivered its cargo into orbit. While many SpaceX fairings have been pulled from the water over the years and put back into service, the ultimate goal is to avoid having to refurbish the components to deal with corrosion caused by salt water - which is expensive and time-consuming.