Deputy Chief Justice Dikgang Moseneke said the division of the estate - provisionally valued at £2.5m excluding royalties - had been accepted by Mandela's family yesterday with no contestation so far.
Mandela's third wife Graca Machel may waive her claims to the estate, Mr Moseneke said at a news conference where he summarised parts of Mandela's 40-page will.
Mr Moseneke said some of the estate would be split between three trusts set up by Mandela, including one designed to provide for his family of more than 30 children, grandchildren and great- grandchildren.
Close personal staff, including his long-time personal aide Zelda la Grange, will each get around £3000 while schools Mandela attended are due to receive £6000.
He also left £6000 to each of four other educational institutions, for bursaries and scholarships.
The mood of the Mandela family when the will was read was "charged with emotions but it went well", said Mr Moseneke, who added that the family were "well pleased" with the contents of the will.
The details were revealed at the Nelson Mandela Foundation in Johannesburg by Mr Moseneke and other executors.
The family trust will receive £82,000, plus royalties from sales of books, including Mandela's autobiography Long Walk to Freedom.
South Africa's ruling ANC will also receive some royalties, to be used at the discretion of the party's executive committee, to spread information about the principles and policies of the ANC, particularly about reconciliation.
The reading of Mandela's will was expected to set off another round of squabbling among members of his large and factious family over the anti-apartheid hero's financial legacy.
Mandela, who died in December at the age of 95, left behind an estate that includes an upmarket house in Johannesburg, a modest dwelling in his rural Eastern Cape home province and royalties.
The home in Houghton, Johannesburg, where Mandela died on December 5 after a long period of ill health, will be used by the family of his son Makgatho, who died in 2005.
The former president had written: "It is my wish that it should also serve as a place of gathering of the Mandela family in order to maintain its unity long after my death."
His legacy includes a potent political and moral brand that some of his grandchildren and great-grandchildren have already used to market everything from clothing to reality TV.
Some of his grandchildren have started a line of baseball caps and sweatshirts that feature his image under the brand Long Walk To Freedom.
Two of his American-based grand-daughters starred in a reality television show called Being Mandela.
Such aggressive marketing - as well as reports of disagreements among family members over Mandela's money - have fuelled the impression in South Africa that some of the family members have exploited their famous relative.
There is a 90-day period in which the will can be contested but Mr Moseneke, who is also deputy head of South Africa's Constitutional Court, said he was not aware of any challenges.
The will was first written in 2004 and last amended in 2008.