"When (Red Bull motorsport consultant) Helmut (Marko) started the call with me I was in my underwear," the 22-year-old told the Red Bull website after the news was announced late on Monday.
"When the call ended I ran around the house shouting to my mates and they all jumped in the pool straight away."
Gasly, the 2016 GP2 champion, was favourite to get the drive after Australian Daniel Ricciardo stunned the former champions just before the August break by announcing he was leaving for Renault.
The rookie, who once looked like he was going to be overlooked by Red Bull, has impressed this year in his first full season with the energy drink company's feeder team Toro Rosso.
Gasly said he was told by Marko before the break that Red Bull were in no hurry to make a decision and to enjoy his holidays.
The Frenchman went to Greece and then returned to the south of France with friends, when Marko called again.
"I was just so shocked. I didn’t really know what I was saying to my mates, so I jumped in the pool and celebrated with my mates and family," he said.
Gasly will be Red Bull's older driver, with Dutch team mate and multiple race winner Max Verstappen still only 20.
"We get on really well and we’ve known each other for a really long time," Gasly said.
"We used to race against each other in karting in 2010 as a junior, so we’ve already raced together, but not for the same team.
"We’ve actually had a couple of close battles, sometimes good for me, sometimes not so good, but we really enjoyed that time."
(Reporting by Alan Baldwin, editing by Ed Osmond)
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