The decision by the US Federal Aviation Administration clears SpaceX to attempt to launch a Falcon 9 rocket carrying 10 Iridium Communications satellites as early as tomorrow.
Musk, who is also CEO of Tesla Motors, has long aimed to reduce the "risk of human extinction" by "making life multiplanetary" by setting up a human colony on Mars.
The FAA, which oversees commercial US space launches, oversaw SpaceX's investigation into why a Falcon 9 rocket burst into flames in Florida as it was being fuelled for a routine prelaunch test on September 1.
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The accident destroyed the $62-million (about R850-million) booster and a $200-million Israeli satellite that had been partly leased by Facebook to expand internet access in Africa.
"The FAA has closed the investigation," the agency said. "SpaceX applied for a licence to launch the Iridium Next satellites from Vandenberg Air Force Base. The FAA has granted a licence for that purpose."
The launch will be SpaceX's first since August. It has a backlog of more than 70 missions for Nasa and other customers, worth more than $10-billion.
As a result of the investigation, SpaceX is changing the way it fuels its rockets to prevent canisters of helium, located inside liquid oxygen tanks, from bursting. It said the long-term solution would be to redesign the canisters. Helium is needed to maintain oxygen tank pressure.
The SpaceX rocket was briefly powered up on Thursday as part of a preflight engine test.
"All systems are go for launch next week," Musk posted on Twitter.
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