Sir Neville started his musical career with the London Symphony Orchestra.
He later established the Academy of St Martin in the Fields, one of the world's leading chamber orchestras.
Its chairman, Paul Aylieff, said Sir Neville's artistic and recording legacy with orchestras and audiences worldwide was "immense".
"He will be greatly missed by all who knew and worked with him and the academy will ensure it continues to be an excellent and fitting testament to Sir Neville," Mr Aylieff added.
A statement from the academy said its founder had passed away peacefully in the early hours of Sunday.
Born in Lincoln in 1924, Sir Neville studied at the Royal College of Music and the Paris Conservatoire.
He first played in a string quartet, then in the London Symphony Orchestra, during which time he decided to form a chamber ensemble from London's finest players.
A group of friends began rehearsing in Sir Neville's front room, before taking their name from the London church of St Martin in the Fields where they staged their first performance in 1959.
The academy, which Sir Neville became life president of, says it now has one of the largest collections of recordings of any chamber orchestra in the world.
Sir Neville has been widely honoured for his work which includes recording the soundtrack for the 1984 film, Amadeus, and becoming the oldest conductor to lead at the Proms, in 2014 at the age of 90.
In March, he was made a Companion of Honour by the Duke of Cambridge at Buckingham Palace, and has also been honoured in France, Germany and Sweden.

It happened at the Moelfre Lifeboat open day at 16:10 BST on Saturday, with two RNLI vessels rescuing him.
He was then taken to Ysbyty Gwynedd, Bangor, by a UK Coastguard helicopter, with his condition unknown.
North Wales Police is investigating the incident and has appealed for witnesses.
Organisers had earlier warned about safety in the water on its Facebook page, imposing a speed restriction on boats travelling to the event.
They had said: "From past experience, we are expected to have over 100 vessels.
"Some will be kayaks with children on board, water safety is very important. Many adults and children will be swimming in the bay. Keep your eyes peeled please."
The event, at the RNLI station, was to allow people to meet the crew and celebrate their life-saving work.

The county council plans to build 200 council homes and 300 affordable homes.
The first will be built on the site of the former Custom House Lane School in Connah's Quay.
Meanwhile, the nearby "old dairy" on Mold Road is being flattened along with some terraced homes on the adjacent High Street. The former dairy has stood empty for more than 30 years.
The council has asked experts to draw up proposals for the site, which will be levelled and seeded once demolition work is completed in March.

The number of corporate insolvencies fell year-on-year by 21%, to stand at 188, in the first three months of 2015.
The figure was 10% lower than the previous quarter.
The number of administrations, which typically affect larger organisations, remained virtually the same as a year ago, with 20 cases.
A quarter-on-quarter comparison showed a similar increase, with two more businesses going into administration in 2015 than the last three months in 2014.
Liquidations, which tend to affect smaller businesses, were down by 24% on a year ago, at 168.
KPMG said the figures suggested the small and medium-sized enterprise (SME) sector was in a healthier economic position as it entered the second quarter of 2015.
Blair Nimmo, head of restructuring for KPMG in Scotland, said: "It's clear as we enter the second quarter of 2015, in general, businesses are in a stronger position.
"Buoyed by an overarching recovery, economically we're seeing a positive trading environment for both large and smaller organisations in Scotland, which is reflected by the drop in insolvency appointments.
"That being said, volatility in oil prices as well as uncertainties around the outcome of the general election may have wider repercussions for the economy as businesses adopt a 'wait and see' approach to growth."
The British conductor and violinist, Sir Neville Marriner, has died at the age of 92, the Academy of St Martin in the Fields says.
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A jet skier has been airlifted to hospital after a crash involving a speedboat during an event off Anglesey.
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Building work is due to start next month on the first new council homes in Flintshire for more than 20 years.
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Fewer Scottish businesses have gone bust since the start of the year, according to new figures from professional services firm KPMG.