Both were on the vessel, Tara, when it ran into trouble between Bokpunt and Gansekraal, at about 04:30 on Monday.
The National Sea Rescue Institute (NSRI) said a 61-year-old Scottish man, and 49-year-old woman from the Republic of Ireland, died in the incident.
A 66-year-old man, also from the Republic of Ireland, made it ashore and raised the alarm.
The South African Maritime Safety Authority is investigating the circumstances which led to the tragedy.
The NSRI - a South African organisation similar to the RNLI in the UK - said its sea rescue rafts and a police dive unit had responded once the alarm was raised.
Rescue teams, however, discovered the yacht broken up among rocks on the shore.
The NSRI said it was not known what had caused the yacht to hit the rocks and whether it had capsized before running aground.
A spokesman said there were three crew members on board, reportedly sailing from Langebaan to Cape Town.
The 66-year-old man who raised the alarm is originally from the Republic of Ireland but resident in the Western Cape.
A Foreign Office spokeswoman said: "We are liaising with local authorities and seeking further information following the tragic death of a British national in Cape Town, South Africa."
A Scottish man and an Irish woman have died after a yacht capsized and broke up on the west coast of South Africa.