The victims were one Japanese man, whose wife survived, and a local tour guide, according to local media, with about 30 rescuers involved in a dramatic 12-hour night operation.
The cable car that takes tourists to the top of the mountain was used to rescue the surviving climber and remove the two bodies from the steep rock face after a helicopter was unable to reach the scene.
About 500 people on the summit were trapped for several hours, with the last group brought down in the early hours of Tuesday after the cable car restarted.
“The crew’s assessment was that the best way to rescue the climbers was to abseil from the cable car,” rescue team spokesman Johann Marais told the Times Live news website.
Marais described the operation as an “extremely difficult rescue” completed during a cold night.
Christmas and New Year are the height of the tourist season in Cape Town, and the cable car is one of the city’s most popular attractions.