Items including Chinese jade and rhino horn were stolen in Cambridge, Durham, Norwich and Lewes, East Sussex.
The men, from Cambridgeshire, Essex, Kent, London, the West Midlands and Northern Ireland, were convicted of conspiracy to burgle.
The case can now be reported after the final four were found guilty.
They were described as some of the gang's "generals", who helped plan and oversee a string of offences.
Richard "Kerry" O'Brien of Dale Farm, Oak Lane, Billericay, Essex, and John "Kerry" O'Brien Junior, Michael Hegarty and Daniel "Turkey" O'Brien, all from Smithy Fen, Cottenham, Cambridgeshire, were found guilty by a jury after a two-month trial at Birmingham Crown Court.
Ten others, dubbed the "Rathkeale Rovers" were convicted at earlier hearings.
The gang was involved in two thefts and an attempted theft at Durham University Oriental Museum as well as further incidents at Gorringes Auction House in Lewes, Norwich Castle Museum and the Fitzwilliam Museum in Cambridge.
Jurors heard exhibits stolen in Durham and Cambridge were valued at about £17m but detectives believed they could have fetched up to £57m ($79m) on the "booming" Chinese auction market.
Lead investigator Det Supt Adrian Green, of Durham Police, said the thefts "dwarfed" the Hatton Garden bank vault raid in which items worth about £14m were stolen.
"If you think the Hatton Gardens break-in was big, this will blow that out of the water," he said.
The most high-profile of the gang's raids involved the theft of Chinese artefacts.
On 5 April 2012, a jade bowl dating from 1769 and a porcelain figurine - which were worth up to £2m - were taken from the Durham museum after thieves smashed a hole in a wall.
They later "hid" the items in a field but were said to have forgotten where. These were recovered and returned to the museum.
Six people were sentenced for the theft, which the judge described as "a complete farce".
Eight days later, on 13 April 2012, 18 mainly jade artefacts were stolen in a raid at Cambridge University's Fitzwilliam Museum. Believed to be worth up to £15m, the items were described as being of "incalculable cultural significance".
Five months later three men were jailed and a boy of 16 was given a detention order. The items have never been recovered.
Despite a number of people being jailed for the various thefts, police said "it soon became apparent an international organised crime group was planning and commissioning the jobs".
Some of the defendants were arrested during co-ordinated raids by officers from 26 forces and the Serious Organised Crime Agency (Soca) in September 2013.
The 40 raids were made in connection with the crimes, which took place between November 2011 and April 2012.
The gang was brought to justice after a four-year covert national investigation - operation Griffin - led by officers from Durham and Cambridgeshire, supported by the National Crime Agency and the National Police Chiefs Council.
The 10 others convicted of conspiracy to burgle included travellers' rights campaigner Richard Sheridan, 47, of Water Lane, Smithy Fen, Cottenham, Cambridgeshire and Donald Chi Chong Wong, 56, of Clapham Common South Side, London.
He was described in court as a "fence" who made frequent trips to Hong Kong. Both denied any involvement in the raids but were found guilty by a jury in November.
Also convicted at the same trial were Alan Clarke, 37, of Melbourne Road, Newham, London; Patrick Clarke, 33, of the same address, John "Cash" O'Brien, 68, of Fifth Avenue, Wolverhampton; Paul Pammen, 49, of Alton Gardens, Southend, Essex; Danny Flynn, 45, of Orchard Drive, Smithy Fen and Ashley Dad, 35, of Crowther Road, Wolverhampton.
Robert Gilbert-Smith, 28, of no fixed address, pleaded guilty to his part in the raids in March last year and has already served his sentence.
Terence McNamara, 46, of Marquis Street, Belfast, pleaded guilty at the beginning of the final trial on 4 January.
The gang members are expected to be sentenced at Birmingham Crown Court on 4 and 5 April.
Fourteen members of an organised crime gang have been convicted over their roles in stealing artefacts worth up to £57m from museums and an auction house.