The Scot, who turned 17 on Friday, came off the bench for an entertaining cameo in the Carabao Cup penalty shoot-out win over League One Derby last Wednesday. He retained his place in the squad for the Premier League fixture against Southampton on Saturday but was an unused substitute.
Doak, who was signed from Celtic for £600,000 in the summer, has impressed in the Anfield youth sides, playing for both the under-18s and under-21s, where he has scored four goals and contributed four assists in helping Liverpool reach the last 16 of the UEFA Youth League.
The youngster has also been called up to the Scotland Under-21 squad for Thursday’s friendly with Iceland at Fir Park.
His new deal at Anfield is believed to run until 2026, which is the maximum possible time for a first professional contract.
“He’s really a lively boy, a smart player, good dribbler, fast, can use both legs,” said Liverpool manager Jurgen Klopp after handing him his debut last week. “He’s good! It was nice to watch, eh? It was really nice to watch, him coming in and immediately a lot of things are obviously natural to him, which is really helpful.
“I’m pretty sure his family was here tonight. I can remember when I saw the family at the AXA when we signed the boy, how excited everybody was. And now having that night, it’s the next step. It’s cool, he showed up, obviously.”