Winstanley heads to Stamford Bridge, where he will link up again with manager Graham Potter, following eight years with the Seagulls, having initially been talent identification manager and then becoming head of recruitment.
"It's not been an easy decision and it has taken me some time, but the opportunity was too great to turn down and is a personal challenge I want to take up," Winstanley said on the Brighton website.
"While I had no desire to leave Brighton, as the club has been amazing to me, this was something I had to pursue."
Winstanley added on the Chelsea website: "There is a real sense of excitement and momentum around the new ownership and this project.
"I am looking forward to working with such an outstanding group of colleagues as the club moves into a new era."
Blues chairman Todd Boehly and co-controlling owner Behdad Eghbali said in a joint statement: "Paul is going to be a great addition to Chelsea.
"He is highly respected and is a key senior addition as we continue to build a world class sporting team with a huge depth of talent, ambition and commitment who will work closely with us to drive Chelsea forward.
"Paul shares our philosophy and will fit seamlessly into the organisation."
Brighton director David Weir commented: "Paul has been an important part of our recruitment and overall progress in his time at the club, and naturally we did not want to see him leave.
"However, we understand that he sees this as an exciting opportunity to move into a more senior position and a different challenge at a new club."