Describing him as the founder of Afghanistan's democracy and a symbol of national unity, Karzai announced three days of national mourning for the former king and ordered flags to be flown at half mast.
James Bays, Al Jazeera's correspondant at the Shah's state funeral in Kabul, said: "The security is tight in Kabul because this is a gathering of Afghanistan's politicians, foreign dignatries, senior figures and tribal elders.
"The funeral proceedings will last a few hours - starting at the Palace, then all of the dignatires, quite remarkably, will walk through the centre of Kabul, to one of the biggest mosques, where prayers will be said for the last king of Afghanistan.
"He is then expected to buried on the edge of town, where the ancestral relatives of the king are all buried."
Zahir Shah ruled Afghanistan from 1933 until he was deposed in 1973. He lived in exile in Italy before returning as an ordinary citizen in 2002.
He came from a long line of ethnic Pashtun rulers and is a distant relative of Hamid Karzai, the Afghan president.
He attended the opening of the loya jirga (grand council) in 2002 and some Afghans were keen to see him returned to power.
The former king's reign is remembered as one of the most peaceful periods of Afghanistan's history.
Born in Kabul on October 15, 1914, Zahir Shah received part of his education in France and returned to Kabul for military training.
He ascended the throne in 1933 after his father was assassinated by a student.
For two decades, he took a back seat, allowing three uncles to run the government. He gradually gained confidence and took control in 1953, overseeing a cautious modernisation of his country.
He supported an end to women wearing the veil, used foreign money to develop the country's infrastructure and balanced rival Soviet and Western interests in his country.
Karzai, the president and a relative of
Zahir Shah, announces the death [Reuters]
In 1973, while on holiday in Italy, he was removed in a bloodless coup by his cousin and brother-in-law, Prince Daoud, bringing to an end two centuries of rule by the Durrani dynasty.
Daoud was later killed in a coup, and after Soviet troops entered the country in 1979 to prop up the communist government, Afghanistan has barely seen peace.
Zahir Shah's wife, Homaira, whom he married in 1931, died as preparations were under way for her to return to Afghanistan to join her husband in 2002.
The couple had five sons and two daughters.