SpaceX achieved history on Sunday with a rocket launch—an act that the CEO of Iridium Communications told CNBC was "critical" to his company's commercial success.

The Falcon 9 rocket belonging to Elon Musk's SpaceX carried 10 communications satellites into orbit from California, merely two days after the company successfully launched a satellite from Florida. The rocket departed from Vandenberg Air Force Base near Los Angeles, carrying a group of new satellites from Iridium.

"SpaceX has been a disruptor of the long-time status quo of the commercial space industry," Iridium chief Matt Desch said. "They are redefining the 'cost to get to space,' and all the other launch providers have had to take note and adjust their plans."

Iridium is SpaceX's largest commercial customer, and the launch from Vandenberg was the second Iridium mission for the commercial space company—part of a contract to deliver 75 Iridium satellites by mid-2018.

However, that timetable is two years behind what SpaceX agreed upon with Iridium in 2010.

"The delays in satellite and rocket readiness for the first launch were frustrating, but fortunately, our current network continued to perform well so we were able to weather the delay," Desch told CNBC.

With a budget of $3 billion dollars, Desch said the program did not incur any additional costs, and the network could still be complete in mid-2018, thanks in part to a tighter-than-expected launch schedule. Iridium's NEXT satellite network will then be able to offer services such as higher broadband communications speeds and global airplane tracking.

SpaceX and Iridium began working over 10 years, and it feels "like we've grown up together," Desch said, as he hailed Musk as "a visionary."

About 20 years ago, Iridium used to launch satellites with SpaceX competitor United Launch Alliance – as well as aboard Russian and Chinese-manufactured rockets. Nowadays, Desch said the current launch industry is very different, and Iridium only works with SpaceX.

"We tried to work with other launch vehicle companies but all were at least twice the cost of SpaceX and unaffordable based on the scope of the network we needed to launch," Desch said, adding that he remains focused on the future.

"I'll be on them Monday to make sure our next six launches over the next 12 months are equally successful. SpaceX isn't 'done' yet," Desch added.

--The Associated Press contributed to this story.