The German philosopher and socialist topped the poll of 20 of the best known, most respected and influential philosophical thinkers.
With 28% of the 30,000 votes cast, Marx, who was championed by author and journalist Francis Wheen, came out as the clear winner.
Marx, who lived in London for many years and based his study of capitalism 'Das Capital' on some of his experiences of industry Britain, had more than twice as many votes as his nearest rival Scottish philosopher David Hume.
Hume, who picked up 12.7% of the vote, was championed in the poll by philosopher and author Julian Baggini.
Coming in third was another German, Wittgenstein, who was championed by Jonathan Sachs and nominated by, among others, Will Self. Wittgenstein garnered 6.8% of the vote.
In Our Time, presented by Lord Melvyn Bragg, ran the online poll over a period of five weeks and attracted more than a million hits to its website.
The programme will be devoting tomorrow's July 14 edition from 9.00-9.45am to a discussion of Marx and his ideas.
The poll sparked a wide-ranging debate with everyone from celebrities to newspapers getting involved.
The Guardian came out in favour of Kant; The Economist, Hume; and The Independent Wittgenstein, then changed its mind, playing on Wittgenstein's famous change of philosophical position.
BBC Radio 2 DJ Terry Wogan backed Marcus Aurelius; Anne Robinson nominated Nietzsche; Mariella Frostrup came out in favour of Kierkegaard; Stephen Fry nominated Plato; and John Humphrys French footballer-turned-actor Eric Cantona.
The 20-strong shortlist was decided after a first round; those with the highest number of votes went through to the next round where they had a specialist advocate, an expert academic who put the case forward for voting for that particular philosopher.
The final stage of the vote began on June 6 when listeners were able to vote for a philosopher from the final shortlist via the Radio 4 website. The vote ended at midnight on July 7.
Since the vote started, the MP3 downloads for 'In Our Time' have increased by 50%. The programme now records 30,000 downloads a week. Half of all downloads across BBC Radio are from the programme.
Before the vote, the 'In Our Time' website was getting 150,000 hits a week, that rose to 300,000 during the vote and has settled to around 220,000 a week now. 'In Our Time' is currently the most popular Radio 4 programme on the internet after 'The Archers'.
Nominee % Accepted votes
1. Marx 27.93%
2. Hume 12.67%
3. Wittgenstein 6.80%
4. Nietzsche 6.49%
5. Plato 5.65%
6. Kant 5.61%
7. Aquinas 4.83%
8. Socrates 4.82%
9. Aristotle 4.52%
10. Popper 4.20%
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