Milner, 40, moves ahead of former Aston Villa, Manchester City and Everton midfielder Gareth Barry.
After breaking into Leeds' team, aged 16, becoming the youngest ever Premier League goalscorer at the time, Milner also enjoyed spells at Liverpool, City, Villa and Newcastle.
He won every trophy available during his time at Liverpool, adding to his two Premier League titles with City.
"He's a role model on the pitch and beside the pitch," said Brighton boss Fabian Hurzeler, who is eight years younger than Milner.
"There's no surprise why he's where he is at the moment because he has such great discipline.
"He has such a great effort every day, and he is never satisfied. He keeps going, and it's a great opportunity for him.
"It's a great day for him to show us again why he is the record-holder regarding the Premier League games."