After inheritance tax is paid, the bulk of it will be divided between her two children Viscount Linley and Lady Sarah Chatto.
The princess died on 9 February at the age of 71.
In her will she made personal bequests to friends and former members of staff, Lord Linley's office said on Tuesday.
Inheritance tax
The Queen was not a beneficiary.
Lord Linley's spokeswoman confirmed the Princess's estate was worth £7,700,176 gross and, after liabilities were paid, £7,603,596 net.
Inheritance tax of 40% will be paid on this, leaving cash and property worth around £4.5m.
The Princess's son and his wife, Viscountess Linley, who had been living at Kensington Palace in Margaret's former apartment, will now be moving out.
Lord Linley moved into Kensington Palace to be near his mother when her health deteriorated.
No decision had yet been made on the future use of the apartment.
Lord Linley's office said the estate was liable to inheritance tax in the same way as any other.
No special concessions had been made, the spokeswoman said.
Will sealed
The remark was made after controversy surrounding the Queen Mother's estate following her death.
Because her wealth passes on to the Queen it was exempt from inheritance tax under an agreement with John Major's government in 1993.
Lord Linley's office said no more details about the will, which was granted probate on Monday, would be made public.
An application in the High Court, before the President of the Family Division, had been approved for the will to be sealed.
The Attorney General, the government's senior law officer, had been consulted and had no objection to the application.