The newspaper editor, 52, was gunned down in the Turkish city on Friday.
Mourners, dressed in black and carrying signs reading "We are all Armenians", crammed the square outside the offices.
Thousands are expected to take part in the funeral march along a five-mile (8km) route to an Armenian Orthodox Church amid tight security.
Turkish prosecutors said the teenager suspected of shooting dead Dink had confessed.
Ogun Samast was arrested after he was identified by his father from CCTV images taken near the murder scene.
He was held in the Black Sea port of Samsun together with six other suspects, before being returned to Istanbul for further questioning.
One of the suspects was named as Yasin Hayal, a friend of Mr Samast, who has spent 11 months in jail for a 2004 bomb attack outside a McDonald's restaurant in Trabzon.
Turkey's Hurriyet newspaper reported on Monday that during police questioning Mr Hayal said that he had given Mr Samast, aged 16 or 17, the gun and the money.
Investigators say that so far they have found no links between Mr Samast and any known political group.
Dink was shot dead in broad daylight outside the office of his newspaper, Agos.
He wrote many controversial articles about the mass killing of Armenians by Ottoman Turks during World War I.
Turkish officials have said the funeral will be held amid high police presence.
"We have cancelled all leave for police and we will have an adequate force in place," Istanbul governor Muammer Guler said on Monday.
Armenian government officials and religious leaders as well as some members of Turkey's Armenian diaspora have been invited to attend the funeral.
Officials from Yerevan will make the trip despite the fact that Armenia and Turkey have no diplomatic relations.
Dink will be buried at Istanbul's Armenian cemetery after a ceremony a religious service and a ceremony outside the Agos office.
Dink's murder shocked Turkey and Prime Minister Erdogan vowed repeatedly that his killer would be caught.
Journalists and politicians in Turkey have expressed outrage at the killing, which many described as a political assassination, while the US, EU, France, and several human rights groups also voiced shock and condemnation.
The issue is a sensitive subject in both Armenia and Turkey. Many Armenians have campaigned for the killings to be recognised internationally as genocide.
Turkey admits that many Armenians were killed but it denies any genocide, saying the deaths happened during widespread fighting in World War I.