The five-time world champions will compete together in the Skud 18 class for a third time.
The Sonar trio of Stephen Thomas, John Robertson and Hannah Stodel represent ParalympicsGB at their fourth Games.
The five experienced sailors join reigning Paralympic champion Helena Lucas, who was selected in April 2015.
It will be the last chance in the immediate future to win medals in the sport after sailing was removed from the programme for the 2020 Games in Tokyo.
Rickham, 34, and Birrell, 29, won silver at the last Worlds in Australia in December.
World champions Robertson, 44, Thomas, 39, and Stodel, 30 made their debut at Athens 2004, finishing sixth both there and in Beijing in 2008.
They were in bronze medal position in London but were given a points penalty after team bosun Simon Hiscocks cleaned the port side of the keel after being authorised to lift the boat out of the water to inspect some damage.
It dropped them down to fifth overall and an appeal to the Court of Arbitration for Sport failed to overturn the decision.
"Representing your country at the Paralympics means the world to us," said Thomas, who also competed in sledge hockey for Britain at the 2006 Winter Paralympics.
"Our sport is incredibly competitive and it's not going to be easy, but going into the competition as reigning world champions definitely gives us confidence."
Sailing team leader Stephen Park says that Rio will test the skills of his squad.
"There's no doubt that Rio is an incredibly challenging environment to compete in, and the sailors will be focusing all their energies on learning the intricacies of racing in Guanabara Bay," he said.
London 2012 bronze medallists Alexandra Rickham and Niki Birrell have been named in Britain's Paralympic sailing squad for this summer's Rio Games.