The alert was raised at 6.30pm last night but rescuers were unable to reach them because of the extreme conditions which saw waves of up to five metres and winds of 120 kilometres an hour.
It was considered too dangerous to try and walk down the mountain at night or to use the emergency helicopter and the sea was too rough for a boat rescue.
The eight tourists, understood to be German, are stranded at the foot of a 200ft ravine known as the Masca barranco, a well-known but challenging beauty spot near Los Gigantes.
The emergency services are currently working out how to get to the stranded tourists who would have had no shelter last night except for finding the cave.
It is believed a local shepherd was on hand to help them.
The rescue mission is being launched this morning by Tenerife fire brigade, the Red Cross and the mountain group of the Civil Guard.
The eight tourists are not thought to have been hurt though weather conditions last night continued to be severe.
Latest reports say they are in good condition and do not need medical attention.
A ferocious storm has ripped through the Canary Island archipelago yesterday, hitting Tenerife, Lanzarote and La Palma the hardest.
Winds reached nearly 70mph in La Palma while a landslide blocks the GC606 road in Gran Canaria.
Photographs showed large trees brought down and sailing boats toppled while stationed on land.
Tenerife’s two airports were closed for more than two hours after torrential rain, and more than 20 flights, largely from the UK and Germany, diverted to neighbouring islands.
Flights to La Palma were also affected, with planes due at the three islands being diverted as far as Agadir in Morocco.
Dozens of flights were affected across the Canaries but they are now operating as normal.
In Tenerife, about 900 holidaymakers couldn’t get home last night and were put up in hotels.
The Canary Government has now lifted its maximum alert but a major mopping up operation had now started.
The emergency services had to deal with hundreds of incidents including landslides, fallen branches, trees on road, demolished roadsigns and power cuts.
Two people had to be rescued when they became trapped in their car in the mountain area of Izaña in Tenerife by snow.
Members of two football teams were also trapped on El Hierro where they had flown for matches but were unable to return when the storms struck.
Several luxury yachts were damaged when battered by the wind in the port of Las Nieves in Las Palmas, Gran Canaria.
(Additional reporting by Rita Sobot)