Ted Briggs, 85, was one of only three of 1,418 crew that survived the sinking during the Battle of the Denmark Strait.
Mr Briggs, from Fareham in Hampshire, passed away at the Queen Alexandra Hospital in Portsmouth on Saturday night.
He was boy signalman aged 18 when the fifth salvo from the Bismarck hit the ship's magazine resulting in a catastrophic explosion. It tore the ship in half and it sank in less than three minutes.
The flagship of the fleet was part of a force ordered to engage the Bismarck and her escort cruiser Prinz Eugen off Greenland.
Mr Briggs was near the bridge when the warship began to roll and he was sucked under by the sinking ship before being propelled back up.
He was soon joined by the only two other survivors; midshipman William Dundass, who died in 1965 and able seaman Bob Tilburn who died in 1995.
The trio spent three hours on the freezing sea before they were picked up by the destroyer HMS Electra close to death.
Briggs, who was president of the HMS Hood Association, described what he saw in the aftermath:
"When I came to the surface I was on her (the Hood's) port side...I turned and swam as best I could in water 4" thick with oil and managed to get on one of the small rafts she carried, of which there were a large number floating around.
"When I turned again she had gone and there was a fire on the water where her bows had been. Over on the other side I saw Dundas and Tilburn on similar rafts. There was not another soul to be seen.
"We hand-paddled towards each other and held on to one another's rafts until our hands became too numb to do so."
In the days after the sinking, Britain's wartime Prime Minister Winston Churchill ordered the Bismarck found and sunk.
On May 27, the battleship was finally sunk after several days of attacks by Royal Navy ships and the Royal Air Force.
Peter Heys, chairman of the HMS Hood Association said: "He was a humorous man but he did not like to be reminded of the sinking as he had to pulled out of the freezing water."
Mr Briggs left the navy in 1973 at the rank of lieutenant and he then became a manager of an estate agents in Fareham. He was awarded the MBE in 1973.
The wreck of HMS Hood was discovered in 2001 and Mr Briggs lay a bronze plaque naming all those who died.
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