Funeral prayers will be held on Sunday evening before several days of public mourning across the country to mark his death.
Flags will be flown at half mast, while government offices and public institutions will be shut as a mark of respect.
King Charles and Queen Camilla paid tribute, saying Sheikh Hamad had “dedicated many years of distinguished service to Qatar”.
“His leadership, vision and commitment to the welfare of the Qatari people were widely admired, both within Qatar and around the world,” they added.
India declared a day of national mourning and said that all entertainment events would cancelled during the period.
Prime Minister Shri Narendra Modi said: “A visionary leader who led Qatar to great levels of development and prosperity.
“We remember him also as a true friend whom I had the honour of meeting during my last visit to Qatar in February 2024.”
When Sheikh Hamad took power 31 years ago Qatar was struggling for money with its oil reserves dwindling.
His coup – carried out while his father Sheikh Khalifa was abroad – changed the country forever.
It became a leading producer and exporter of liquefied natural gas, thanks to international partnerships and investments that had been brokered.
In 1996 Al Jazeera was launched there before becoming a big name in international broadcasting.
And Sheikh Hamad founded the Qatar Investment Authority which put money into businesses abroad, including Harrods and football team Paris Saint-Germain.