Around the time of the summer break, Albon was promoted from Toro Rosso to replace the underperforming Gasly, who went in the other direction.
The 23-year-old hasn't claimed a podium spot yet, but has regularly finished fourth or fifth, giving Red Bull enough encouragement that he is ready for a full season, starting in 2020.
“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," Red Bull team principal Christian Horner said after the announcement on Tuesday.
"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.”
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