Both venues will be hosting the Senior Open for the second time, with American Loren Roberts taking the title on Sunningdale's Old Course back in 2009, defeating compatriot Fred Funk and Ireland's Mark McNulty in a play-off.
Bernhard Langer won his first senior major at Carnoustie in 2010, edging out 2010 US Ryder Cup captain Corey Pavin by a shot.
The Senior Open Championship at Royal Birkdale last year attracted record crowds of 45,575 as Mark Wiebe defeated Langer in a five-hole play-off.
"After a hugely successful Senior Open at Royal Birkdale we are very much looking forward to taking the Championship to two outstanding venues in Sunningdale in 2015 and Carnoustie in 2016," Johnnie Cole-Hamilton, Executive Director of Championships at the R&A, said.
"Both are iconic courses and have successfully staged The Senior Open Championship once before, so the players will look forward to returning to them."
This year the top players over the age of 50 in the world will pull on their golf clothing at Royal Porthcawl in Wales.
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