Trevor Francis became the first £1m men’s player when he joined Nottingham Forest 46 years ago.
Smith, who only turned professional in 2023, joined Liverpool from Portuguese side Sporting a year ago for a club record fee of just over £200,000.
Arsenal head coach Renee Slegers said Smith is an “exciting young player” who can make a “big contribution”.
She scored seven goals in 20 Women’s Super League games in her debut season as Liverpool finished seventh.
Liverpool are without a manager since sacking Matt Beard in February, with former Manchester City boss Gareth Taylor the leading candidate to take over.