He was born in London and studied chemistry and metallurgy at the Royal School of Mines. He emigrated to Victoria, Australia in 1852, then moved to Otago in 1861, where he was the first editor of the Otago Daily Times.
He first became involved in politics in 1863, holding a variety of appointed and elected posts. He was premier 1873 to 1875 and again in 1876. During his political career, Vogel worked for reconciliation with Maori, an effort generally regarded to be successful. In 1887, he introduced the first Women's Suffrage Bill to Parliament, although suffrage was not actually granted until 1893. Vogel was knighted in 1875.
Vogel is also reputed to be the first New Zealander to write a science fiction novel; Anno Domini 2000 - A Woman's Destiny, published in 1889. It anticipated a utopian world where women held many positions of authority. Interestingly, New Zealand was the first country to give women the vote and by 2000 was largely governed by women (as the Governor-General, Prime Minister, Attorney-General and Chief Justice are all women).
The New Zealand fan awards for science fiction writing are named in his honour. Vogeltown, a suburb of New Zealand's capital city, was also named for him.