President Aziz landed at the Matsapha International Airport on Wednesday and attended a banquet at the Lozitha Royal Palace.
He is one of several guests for King Mswati III's 51st birthday celebrations scheduled for Friday at the Buhleni Royal Residence stadium.
The king was born on April 19, but this year's celebration was shifted because his birthday coincided with the Good Friday services where royalty also participates.
While in eSwatini, President Aziz will tour several agricultural projects and sugar mills.
He will depart on Saturday April 27.