Usama al-Bar, who heads a government centre that helps organise the annual five-day pilgrimage, said: "The first stage of the projected overhaul of Jamarat Bridge in Mina began on Saturday and will be completed and ready for next year's Hajj,"
Scores of pilgrims were crushed to death as they jostled to perform a stoning ritual at the bridge on Thursday, the last day of this year's Hajj when more than two million Muslims converge on Saudi Arabia.
In 2004, a similar incident claimed the lives of about 250 pilgrims at the same site.
A decade earlier, 270 were killed in a similar stampede.
Thursday's toll was the highest since 1426 people were killed in a stampede in a tunnel in Makka in 1990.
Pilgrims stone the three pillars
representing the devil
The authorities had already said they would replace al-Jamarat Bridge with an elaborate system of entrances and exits, including a subway, which will cost 4.2 billion riyals ($1.12 billion).
The project will take three years to complete.
The first stage, which will be ready for the next Hajj, involves a two-storey bridge and an underground emergency exit for pilgrims and ambulances.
Al-Bar said the development would allow Saudi Arabia to host more than the 2.5 million pilgrims it currently allows in.
The bridge is 32-years-old, and the legitimacy of Saudi Arabia's ruling family for many Muslims rests on its ability to host pilgrims every year from all over the world.