The instrument, found strapped to the body of Wallace Hartley after he drowned along with 1,500 others in the disaster in 1912, was sold at Titanic specialist auctioneers Henry Aldridge and Son in Devizes, southwest England.
The instrument carries an inscription from the 33-year-old's fiancee Maria Robinson to mark their engagement and was on sale with its leather luggage case, initialed W.H.H, in which it was found.
For decades the violin was believed lost but it was found in the attic of a house in northwest England in 2006, prompting a debate about its authenticity, which experts only recently resolved.
Bidding started at just £50 for the violin, but within a few minutes it had passed the previous world record of £220,000 for a Titanic piece as competition between four telephone bidders hotted up.
There were gasps from the 200 people at the auction house as the price reached £350,000 and then a tense silence as the battle for the instrument narrowed to two telephone bidders.
It took just 10 minutes to sell it for its final price.
Hartley's band played the hymn "Nearer, My God, To Thee" to try to calm passengers while they climbed into lifeboats as the Titanic sank beneath the icy waves in the North Atlantic on April 15, 1912, after hitting an iceberg.
Hartley and his seven fellow band members all died after choosing to play on.