Since giving up his membership last year to focus on the PGA Tour, the 38-year-old Englishman has climbed from 75th to 24th in the world rankings.
Casey said staying in America was the "right decision for my family" but he was "very sad" he would not be able to qualify for Europe's Ryder Cup team.
Europe captain Darren Clarke said Casey's decision was "disappointing".
Clarke can only select players who hold European Tour membership.
Former world number three Casey played in Europe's nine-point victories in 2004 and 2006, and their defeat at Valhalla in 2008.
He was left in tears when he was overlooked for a wildcard by Colin Montgomerie in 2010, when he was ranked seventh in the world.
Casey said: "With my wife and young son as my priority, I have decided to continue to concentrate on the PGA Tour, which has worked well for us this past year.
"I believe this decision will help me to be the best I can be both on and off the course."
Clarke, who played alongside Casey at Oakland Hills in 2004 and the K Club in 2006, said: "It is obvious that representing Europe in the Ryder Cup is not on Paul's priority list, which is disappointing, but I wish him all the best for the future.
"The focus is firmly on the players who are committed to the European cause as we move towards Hazeltine and I look forward to working with these players over the next 10 months."
The 2016 Ryder Cup begins on 27 September.
Paul Casey has ruled himself out of the 2016 Ryder Cup by deciding not to rejoin the European Tour.