The vote was carried by a show of hands at a well-attended extraordinary general meeting in London. Some 90 per cent of proxies also voted in favour.
Shares in the two businesses will start trading on Monday. Shares in the larger EMI group, which will include the HMV records chain, are expected to start trading at around pounds 14. The smaller Thorn division, which includes the Radio Rentals and Crazy George's businesses, is expected to see its shares open at around 410p.
As a result of the demerger, Thorn EMI will disappear from the FT-SE 100 list of leading shares, but both of the demerged businesses will join the top tier. Cookson, the engineering and ceramics group, will be removed to make way.
On its last day of trading Thorn-EMI shares rose strongly, finishing the day 44p higher at pounds 18.33.
Addressing shareholders at the meeting, Thorn-EMI chairman Sir Colin Southgate said he expected shares in EMI group would be "very highly rated" when they start trading. "If not, I'll be very disappointed."
Some shareholders questioned the wisdom of the de-merger, but Sir Colin said it would unlock shareholder value. He said both businesses would grow faster outside of the group. "Thorn will come out from under the umbrellas of EMI, which is a glamourous business. It will develop its own strategy and strengths and drive forward faster."
Sir Colin also told the meeting that adviser fees for the de-merger had totalled pounds 70m - a relatively small sum for a company valued at pounds 8bn, he said.
Some analysts regard the EMI business as a takeover target at a possible figure of pounds 20 per share. The Thorn rental business is, however, earmarked for more pedestrian growth.