His contributions to the field included work on the EDSAC and the Burrows-Wheeler transform. Along with Maurice Wilkes and Stanley Gill he is credited with the invention of the subroutine (which they referred to as the closed subroutine), because of which jump to subroutine instruction is often called Wheeler Jump. In cryptography, he was the designer of WAKE and the co-designer of the TEA and XTEA encryption algorithms together with Roger Needham.
Wheeler married Joyce Blackler in August 1957, who herself used EDSAC for her own mathematical investigations as a research student from 1955. He became a Fellow of Darwin College, Cambridge in 1964 and formally retired in 1994, although he continued to be an active member of the University of Cambridge Computer Laboratory until his death. In 1994 he was inducted as a Fellow of the Association for Computing Machinery. In 2003 he was a Computer History Museum Fellow Award recipient.
Wheeler is often quoted as saying "Any problem in computer science can be solved with another layer of indirection. But that usually will create another problem." Another quotation attributed to him is "Compatibility means deliberately repeating other people's mistakes."