Albon replaced Gasly from the middle of the season, joining Red Bull for the Belgian Grand Prix, after a series of unconvincing performances by the Frenchman in the first half of the season.
Since then, an impressive run of results has helped him finish in the top six in every outing for the team so far.
The announcement concludes a remarkable 12 months for the Anglo-Thai driver, who looked set for a season in Formula E with Nissan this time last year.
He was then announced as Kvyat’s team-mate at Toro Rosso, before being promoted to Red Bull.
Albon’s wheel-to-wheel prowess and consistent results impressed Red Bull team principal Christian Horner, who said that his results were key to his retaining of the seat.
“Alex has performed extremely well since his debut with the team in Belgium and his results – seven finishes in the top-six – speak for themselves,” Horner said.
“It’s extremely hard to deny that level of consistency and in tandem with a growing reputation as a tenacious, fiercely committed racer, Alex has proved that he fully deserves to continue his progress with Aston Martin Red Bull Racing.
“There is plenty of potential still to unlock and we look forward to seeing Alex alongside Max in 2020.”
Albon said he was looking forward to continuing with Red Bull.
“I am really excited to be partnering Max again for next year and I know how fortunate I am to be given this opportunity.
“I’m hugely thankful that Red Bull have put their trust in me and believed in my results since I joined the Team and for them to keep me in the car next year is a big deal.
“This year has been an incredible year for me and getting the call up to Red Bull mid-season was already a big step, so now I will use the learnings from this season and use the experience to improve and fight at the front in 2020.”