The English links of Birkdale, in Southport, has staged nine previous Opens, the last in 2008. Carnoustie, in Scotland, has been the venue on eight occasions.
"I am delighted to see the Open returning to two great venues," said Tom Watson who won the event five times in total and once apiece at the two courses.
"When I first played at Carnoustie I still had a lot to learn about links golf but I quickly adapted to the challenge of playing in the wind and keeping the ball low," the American said in a statement.
"Birkdale is also a fine links course and I have always thoroughly enjoyed playing there. I think the players and the fans will be excited to see the top players playing these courses once again."
This year's Open begins at Royal Liverpool in Hoylake on July 17.
(Reporting by Josh Reich, editing by Tony Jimenez)
