Mark Cunningham, QC, appearing for NatWest, told Mr Justice Warren that the estate was worth £2,042,000 - with £1,033,000 to be paid to claimants and £689,000 to their representatives.
Because of other costs, the amount left will be about £141,000 - which will be divided among defendants such as the BBC, the NHS and Barnardo's, which had already paid out damages.
Savile had an estate reported to be worth about £4m when he died in 2001 aged 84 without ever facing prosecution.
It emerged after the Jimmy Savile's death that the paedophile broadcaster had assaulted hundreds of children. He sexually assaulted victims as young as five at NHS hospitals during decades of unrestricted access, reports say.
He abused 63 people, who were aged between 8 and 40, connected to Stoke Mandeville Hospital from 1968 to 1992, according to the Stoke Mandeville report.
Claimants and their solicitors can expect their payments next week after a written judgment, though Justice Warren has said he will grant the application.
Peter Saunders, founder of the National Association for People Abused in Childhood, told the Sunday Times: 'Arguably the only people who really win in these situations are the lawyers - they take the lion's share of the money in estates such as Savile's.'
John Mann, the Labour MP who has campaigned against child sex abuse, called the sum an "absurdly large amount".
Liz Dux, specialist abuse lawyer at Slater and Gordon who represented 168 of Savile's victims, said: "What has been most important in all of this was that those Savile victims whose claims have been accepted, will receive their compensation in full. There will be no deductions.
"All parties including the Savile Estate wanted this matter concluded as quickly and cheaply as possible but the actions of the Savile Trust, who were the beneficiaries under his will, have been to constantly try to block the victims receiving a penny in compensation.
"Sadly, it has been the actions of the beneficiaries of the estate which has led to the escalation of costs due their continued opposition of the settlement scheme. Fortunately, the Courts have defeated their efforts. Justice has prevailed and those who Savile abused can now hopefully achieve closure."
Osborne Clarke's costs for Thursday's two-hour High Court hearing were said to be £61,000, however, a spokeswoman for the firm said the sum did no represent costs for the hearing.
They claimed the firm's fees "comprised less than half the figure" and were not just for the two-hour hearing, but for the necessary work taken to make the application.
They added that under the scheme, 166 claimants will be receiving £2,306,636 - a figure covering claims against the estate, NHS, BBC, Barnardo's and mental health charity MIND - not those solely against the estate.
The law firm said: "The £1.8m figure is inaccurate as taken out of context, and does not represent only Osborne Clarke fees, which are only a proportion of the overall figure."
The overall sum included third-party costs.
