The vehicle plunged down an embankment, according to the emergency services on the Atlantic island, which is part of Spain and popular with tourists.
In addition to the man who was killed, 27 other people were injured, three of them seriously.
"The person who died was a 77-year-old British man," the Spanish Civil Guard told Reuters.
Photographs shared by the Canary Islands government on social media appear to show the bus had come off the road at a hairpin bend, coming to rest in a ravine.
The accident reportedly occurred in the early afternoon not far from the island's capital, San Sebastián de La Gomera.
The vehicle is said to have veered off the road and plunged down a slope.
The cause of the accident was initially unclear.
Numerous emergency services were at the scene, including paramedics, the fire brigade and the Guardia Civil police unit, as reported by the regional newspaper Canarias7.
A rescue helicopter is assisting with the recovery and transport of the injured.
La Gomera is among the smallest of the Canary Islands, with steep terrain marked by volcanic mountains, dense forest and cliffside villages.
The islands, known for their year-round warm temperatures, are popular holiday destinations for many Europeans.
with PA and AP
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