The Canada Under-20 international arrived at the club’s Kirkby academy base towards the end of last season after leaving Fulham.
A regular member of Neil Critchley’s Under-18s, he impressed in pre-season and scored a hat-trick on his debut in the first game of 2016-17 against Blackburn Rovers.
Liverpool have now demonstrated their commitment to the rising star by tying him down to his first professional contract at the earliest opportunity.
When asked about Millar last month, Under-18s manager Neil Critchley said: “What I like about him is he can run down the side of defenders, he runs in behind, he gives them real problems with his movement and he’s a good finisher off both feet.
“We’ve been extremely pleased with him since he’s come in, he’s settled into the group straight away, it’s like he’s been here for years.
“He’s got a good brain, good awareness, very calm and can finish. He’s a good player, a good all round player.”
In other Liverpool transfer news, a senior club figure has agreed a shock move to the Bundesliga.