Earps, 22, missed just one game in two seasons at Bristol and has previously played for Doncaster Belles, Nottingham Forest and Birmingham City.
She joins Reading ahead of their first WSL 1 campaign following their promotion from WSL 2 last season.
"The club has a lot of ambition and a great work ethic, it's a really exciting opportunity for me," she said.
Reading women have signed former Bristol Academy and England Under-23 goalkeeper Mary Earps.