Arsenal's blockbuster move eclipses the previous record set by American defender Naomi Girma's 900,000-pound transfer from San Diego Wave to Chelsea in January, although the 25-year-old had already broken the one million dollar mark.
The first player in men's football to command a million-pound price tag was former England forward Trevor Francis when he moved from Birmingham City to Nottingham Forest in 1979.
“It’s my dream to compete for the biggest titles here in England and in Europe, and I’m excited to get started and contribute to doing that here with Arsenal," Smith said in a statement.
The versatile Smith, who can operate as a striker or play on the wing, enjoyed a stellar debut season at Liverpool despite the club's struggles.
Smith finished as Liverpool's leading scorer across all competitions with nine goals to claim their player of the season award, even as Liverpool slumped to seventh in the Women's Super League after a fourth-placed finish the previous campaign.
Arsenal are building on their Champions League triumph with ambitious recruitment, having already bolstered their squad by re-signing Chloe Kelly from Manchester City as a free agent.
They also snapped up left-back Taylor Hinds from Liverpool after her contract expired.
But securing Smith represents a statement of intent from Renee Slegers's side, who finished as runners-up to Chelsea in the league.