The 18-year-old striker has been rewarded with an extended contract at the end of his breakthrough season for Southampton, having made 19 appearances in all competitions.
Gallagher netted his first senior goal for the club against Yeovil Town in January and broke his Premier League duck in the 4-2 win over Norwich City in March.
Having committed to Southampton on a long-term basis, the teenager is now relishing the prospect of continuing his development under manager Mauricio Pochettino.
"I'm very happy and very proud. I won't forget this day," Gallagher told the club's official website.
"This time last year I'd have never really thought I'd be getting this contract yet.
"I thought I'd have to battle it out to get one, but this gives me that bit of security so I know that, if I can keep going, the club will repay me.
"I don't really think I've had time to think about how far I've come this year
"I'm still getting a lot of experience, even from training and being around everyone.
"Now it'll be good to see how I push on next season. I'm looking forward to pre-season because it's my first one with the first team."
