Ricciardo has already announced he is moving to Renault, leaving a vacancy alongside 20-year-old Dutch driver Max Verstappen.
"Since Pierre first stepped into a Formula One seat with Scuderia Toro Rosso less than a year ago he has proved the undoubted talent that Red Bull has nurtured since his early career," said team boss Christian Horner in a statement.
"His stellar performances this year at the Honda-powered team, in only his first full season in Formula One, have only enhanced his reputation as one of the most exciting young drivers in motorsport."
Gasly won the GP2 (now Formula Two) title in 2016 and made his F1 debut with Toro Rosso in Malaysia late last year before starting his first full season in March.
The 22-year-old had been the obvious candidate to replace Ricciardo, with Red Bull-owned Toro Rosso the feeder team for the Austrian energy drinks company's main outfit.
He finished an impressive fourth in Bahrain and has two further top 10 finishes to his credit from the first half of the campaign.
Toro Rosso are powered by Honda, whose engines will also be used by Red Bull from next season following the split from Renault.
"To be awarded a drive at Aston Martin Red Bull Racing from 2019 is a dream come true for me," said Gasly in the team statement.
"It has been my goal to race for this team since I joined the Red Bull Junior Driver Programme in 2013, and this incredible opportunity is another step forward in my ambition to win Grands Prix and compete for World Championships."
His promotion leaves Toro Rosso with at least one vacancy for 2019 and possibly two given the uncertainty surrounding New Zealander Brendon Hartley's future.
Gasly has scored 26 points to Hartley's two so far but the 28-year-old Kiwi could be kept on given the lack of ready alternatives from within the Red Bull young driver programme.
(Reporting by Alan Baldwin; Editing by Alison Williams and Ken Ferris)
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