Supreme Leader Ayatollah Ali Khamenei, who holds supreme authority in Iran, declared five days of national mourning and handed interim charge to Vice President Mohammad Mokhber, 68, ahead of the election.
State media later announced that the presidential election would be held on 28 June.
Iran's top nuclear negotiator Ali Bagheri, who served as Amir-Abdollahian's deputy, was chosen to serve as acting foreign minister.
After leaving Tabriz, Raisi's body will reach Iran's Shia clerical center Qom on Tuesday before being taken to Tehran.
Khamenei is due to deliver prayers at a farewell ceremony in Tehran on Tuesday night, ahead of major processions starting on Wednesday morning.
Raisi will then be taken to southern Khorasan province on Thursday morning and later to his hometown Mashhad, where he will be buried on Thursday evening after the last rites.
The 63-year-old ultraconservative Raisi has been in office since 2021, during which time Iran has been rocked by mass protests, an economic crisis worsened by US sanctions and armed exchanges with arch-foe Israel.
Raisi replaced moderate Hassan Rouhani at a time when the economy was hit by US sanctions over Iran's controversial nuclear programme.