The National Accountability Bureau (NAB) court handed down the verdict after a series of delays.
His daughter, Maryam Nawaz Sharif, received a seven-year sentence, while his son-in-law, Safdar Awan, was given a one-year sentence.
Nawaz Sharif has said the charges are politically motivated.
Both he and his daughter are in London, where Sharif's wife, Kulsoom Nawaz, is receiving treatment for cancer.
Judge Mohammad Bashir ordered Sharif to serve 10 years for owning assets beyond income and one year for not co-operating with the NAB. He will serve his sentences concurrently.
Daughter Maryam received seven years for abetting a crime and one year for not co-operating - again to run concurrently - while Safdar Awan's sentence is for not co-operating.
Sharif and Maryam also received fines of £8m ($10.6m) and £2m respectively.
The case, known as the Avenfield Reference, relates to a number of properties in the UK capital.
The Panama Papers leak in 2015 revealed several of Sharif's children had links to offshore companies, which were allegedly used to channel funds and buy foreign assets - including luxury flats in Avenfield House, on London's Park Lane.
His family, however, insist they legitimately acquired the four properties.
As part of the ruling, the court ordered they be confiscated for the federal government.
Members of the Pakistani media set up outside the Avenfield House properties, where the family reportedly watched the verdict:
The country's Supreme Court ousted Nawaz Sharif from the premiership in July 2017 following the Panama Papers revelations.
At the time, he was less than a year away from becoming the first head of government in Pakistani history to complete a full term in office.
Sharif held the office from November 1990 to July 1993 and from February 1997 until he was toppled in a bloodless coup in October 1999.
