Morris secured a spot with victory in her semi-final at the World Championships in Aiguebelette, France.
The former Para-cycling champion was joined in reaching Rio by fellow single sculler Tom Aggar, third in his semi.
GB's mixed four of Grace Clough, Dan Brown, Pamela Relph, James Fox and cox Oliver James, also qualified.
Their semi-final victory ensured all three boats have reached next year's Games, along with the mixed double scull team of Laurence Whiteley and Lauren Rowles who won their repechage on Tuesday.
Of her win, Morris - a 2008 Paralympic hand-cycling gold medallist - said: "I am really pleased with that. Eighteen weeks ago I had shoulder surgery so the aim here has always been to qualify the boat for the Games. "
Rachel Morris capped her successful return from shoulder surgery as three more Great Britain boats qualified for the 2016 Rio Paralympics.