In making the announcement, Perak Menteri Besar Zambry Abdul Kadir said the ruler died at 1.30pm at the National Heart Institute in Kuala Lumpur.
His remains will be taken to the palace in Kuala Kangsar tomorrow morning and buried at the royal mausoleum there after Asar (mid-afternoon) prayers.
Tomorrow will be a public holiday in Perak as the state will be in mourning.
No entertainment or celebrations will be allowed in the state for seven days until June 4.
The Malaysian flag will also fly at half mast until June 4, while the Perak flag will fly half mast for 100 days starting today.
"May Allah bless his soul," Zambry said.
A lawyer, judge and sportsman
Azlan Shah was sultan of Perak for 30 years and reigned as Yang di-Pertuan Agong from 1989 to 1994.
He is survived by his consort Tuanku Bainun Mohd Ali, two princes and two princesses. Another prince, Raja Ashman Shah died on March 30, 2012.
Before becoming the sultan of Perak, Raja Azlan, a lawyer, served as a judge and Lord President of the Federal Court.
In 2009, the late sultan (right) played a key role in the Perak constitutional crisis when he declined then menteri besar Nizar Jamaluddin's request to dissolve the state assembly, following defections.
Instead, he directed Nizar to resign as Nizar had lost confidence of the House.
BN, with support from three defected Pakatan Rakyat assemblypersons, formed a new government thereby toppling the elected Pakatan government.
The matter was later taken to court with a five-member bench at the Federal Court declaring in 2010 that BN's Zambry was the rightful menteri besar.
The court found that the Perak Constitution gives absolute discretionary powers to the sultan to withhold consent to dissolve the state assembly.
Raja Azlan also made significant contributions to the sport of hockey, and was president of the Asian Hockey Federation and executive board member of the International Hockey Federation.
The Sultan Azlan Shah Hockey Tournament is hosted annually in the Perak capital of Ipoh.