Businessman Alistair Cook had just sent a text message to his wife Vicky, telling her his achievement when he suffered a fatal heart attack, the Daily Express reported.
An experienced hiker, Cook said he felt "exhausted but so happy" after reaching the 5,895-metre-high summit. The expedition was arranged to mark his coming 70th birthday.
He was the first of a five-member team to reach the top of the mountain in Tanzania.
He undertook the mountain trek with four other climbers as part of a trip organised by Team Kilimanjaro, a company which specialises in climbing holidays. The incident happened on the descent.
"A lady he was climbing with told me he said to her, 'It's the hardest thing I have ever done, but I feel ecstatic'. I think that is a great tribute to Alistair and the man he was. He had lots of energy and enthusiasm -- a passion for life," Cook's wife Vicky said.
Cook had trained for about 18 months for the climb, and walked near his home every morning. He had also scaled Mount Snowdon in Wales, in preparation for the challenge.
Cook was an engineer by trade, but founded a picture-framing firm in Leicestershire 34 years ago.