The England Under-21 international was the one of the few shining lights in a gloomy season for the Black Cats, who managed just six wins from their 38 league games.
Pickford was kept busy and showed his prowess with 135 saves - the second-most in the top flight - which included four clean sheets, leading to interest from elsewhere.
The Merseysiders moved quickly to complete the transfer which sees Pickford move to Goodison Park on a five-year contract for an initial fee of £25 million that could rise to £30m based on performances.
The 23-year-old becomes the third-most expensive keeper in football, behind new Manchester City signing Ederson (£34.7m) and Juventus icon Gianluigi Buffon (£32.6m).
"It's great to sign for the club. Last season was my first in the Premier League so to get this opportunity with Everton now, to be able to go forward with my career and show everyone what I can do with Everton is unbelievable," he told the club's official website.
"It's a great club, a massive club and I think it's a great opportunity and the right time for me to come to Everton and show what I can do. This is an exciting time for the club and for me, too, with the ambition being shown. I just want to be the best I can be to help.
"I've just got to show people what I can do, keep training and working hard and when it comes to game day, produce what I can do - making match-winning saves, showing what my distribution is like and making the right saves at the right times."
Toffees boss Ronald Koeman added: "I'm really pleased we've made what I'm sure will be a significant signing for Everton Football Club.
"Jordan is a very talented young professional who also has a real hunger for success, and that's important for us as we now look to make further progress in the seasons ahead.
"We've seen the quality he has through his performances in the Premier League last season and, given his young age, we're sure he will get even better."