During the rocket's first launch in 2018, the side boosters made it, but the center core missed its drone ship landing.
About 34 minutes after liftoff, the shiny silver satellite was successfully deployed. Eastern from Space Launch Complex 39A in Cape Canaveral Air Force Station in Florida, with the 6,460-kilogram Arabsat-6A.
The roads were also jammed for Wednesday night's launch attempt, which was scuttled by high winds.
Falcon Heavy has already been chosen for a few contracts, including a $130 million contract to launch an Air Force satellite that was awarded just four months after its inaugural flight in February 2018.
Until SpaceX came along, boosters were discarded in the ocean after satellite launches.
The job was to place the six-ton Arabsat-6A satellite into geostationary orbit about 22,500 miles (36,000 kilometers) above the Earth. The boosters can then be refurbished and used again, which SpaceX says drastically reduces the cost of spaceflight.
Minutes after launch, the two side cores dropped away and descended to make separate touchdowns at two landing zones on the Florida coast, not far from the launch pad.
In Falcon Heavy's first launch, in February 2018, a dummy dubbed Starman was placed behind the wheel of Musk's roadster, which is now orbiting the Sun somewhere between Earth and Mars.
The satellite aims to provide communications to people in the Middle East, Africa, and Europe.
SpaceX landed three of its Falcon Heavy rocket boosters for the first time on Thursday, as part of a mission which was delayed from the day before due to bad weather.
Saudi Arabia-based Arabsat announced plans to launch with SpaceX in spring 2015, but at the time hadn't decided between the Falcon 9 or Falcon Heavy.
Falcon Heavy is not expected to fly almost as often as its smaller counterpart, which has completed more than 20 missions since last February. The Falcon Heavy is essentially three of those single rockets strapped together.