The pair, who compete in the Para-rowing mixed double scull, secured the place by winning the repechage to make the World Championships final in Aiguebelette, France.
Rowles, 17, is a former wheelchair track racer who represented England at the Commonwealth Games in Glasgow.
She took up rowing earlier this year.
Whiteley, 24, who trained without a partner for two years while he waited for a suitably classified female partner to be found, said: "I've spent two and three quarter years waiting for this moment. Our goal here was to qualify and it feels great."
Laurence Whiteley and Lauren Rowles have become the first British rowing team to qualify a boat for the 2016 Paralympics in Rio de Janeiro.