The pilgrimage consists of a series of religious rites which are completed over five days in Islam's holiest city and its surroundings in western Saudi Arabia.
On Thursday, the pilgrims will move to Mina, around five kilometres (three miles) away from the Grand Mosque, ahead of the main rite at Mount Arafat, where it is believed the Prophet Mohammed delivered his final sermon.
Four hospitals and 26 health centres are ready to treat pilgrims in Mina, state media said.
This year's hajj is restricted to vaccinated Muslims under the age of 65 chosen from millions of applicants through an online lottery system.
Those coming from outside Saudi Arabia were required to submit a negative Covid-19 PCR result from a test taken within 72 hours of travel.
Since the start of the pandemic, Saudi Arabia has registered more than 795,000 coronavirus cases, more than 9,000 of them fatal.
Those attempting to perform the hajj without a permit face fines of 10,000 Saudi riyals (around $2,600).
Policemen in the mountainous city have set up checkpoints and conducted foot patrols.
Some pilgrims have donned clothing featuring the names and flags of their countries. "Hajj 2020 -- Chad" was written on the back of the white robes of one group.
Hosting the hajj is a matter of prestige and a powerful source of political legitimacy for Saudi Arabia's rulers.
Costing at least $5,000 per person, the hajj is also a money-spinner for the world's biggest oil exporter, which is trying to diversify its economy.
In normal years, the pilgrimage brings in billions of dollars.
These days it represents a chance to showcase the kingdom's ongoing social transformation, despite persistent complaints about human rights abuses and limits on personal freedoms.
Saudi Arabia now allows women to attend the hajj unaccompanied by male relatives, a requirement that was dropped last year.