Iridium's next-generation global satellite constellation will deploy a cross-linked low-Earth orbit architecture, covering 100 percent of Earth's surface.
The process of replacing the satellites one by one in a constellation of this size and scale has never been completed before.
SpaceX initially aimed to launch the Iridium-5 mission on March 29, but a technical glitch with one of the satellites forced a delay.
The launch on March 30 is one of two missions in four days for SpaceX. Another used the Falcon 9 rocket to launch an uncrewed Dragon cargo ship, which has flown previously, to deliver cargo to the International Space Station.
The U.S.-based National Aeronautics and Space Administration's (NASA) cargo mission was launched on Monday from the Cape Canaveral Air Force Station in Florida, with Dragon arriving at the space station shortly after.
Under an agreement with NASA, SpaceX is now developing the refinements that will enable Dragon to fly crew. Dragon's first manned test flight is expected to take place as early as this year, according to SpaceX.
The top U.S. telecommunications regulator on March 29 gave formal approval to a plan by Elon Musk's SpaceX to build a global broadband network using satellites.
"This is the first approval of a U.S.-licensed satellite constellation to provide broadband services using a new generation of low-Earth orbit satellite technologies," the Federal Communications Commission (FCC) said in a statement.
The system, proposed by privately held SpaceX, will use 4,425 satellites, the FCC said.
FCC Chairman Ajit Pai in February endorsed the SpaceX effort, saying that "satellite technology can help reach Americans who live in rural or hard-to-serve places where fiber optic cables and cell towers do not reach."
SpaceX successfully launched its Falcon 9 rocket on Monday at Cape Canaveral, which then deployed the company's Dragon capsule into orbit, industry website theverge.com reported.
The FCC said SpaceX has been granted authority to use frequencies in the Ka (20/30 GHz) and Ku (11/14 GHz) bands.
Musk, who is also the founder and chief executive of electric automaker Tesla Inc, said in 2015 that SpaceX planned to launch a satellite-internet business that would help fund a future city on Mars.
SpaceX wanted to create a "global communications system" that Musk compared to "rebuilding the internet in space." It would be faster than traditional internet connections, he said.
"This is an important step toward SpaceX building a next-generation satellite network that can link the globe with reliable and affordable broadband services, especially reaching those who are not yet connected," SpaceX Chief Operating Officer Gwynne Shotwell said.