The World Health Organization (WHO) programme aims to ensure that vaccines are shared fairly among all nations.
Covax is aiming to deliver about two billion doses of Covid-19 vaccines globally by the end of the year.
A total of 600,000 doses of the vaccine developed by AstraZeneca and Oxford University arrived in Ghana's capital Accra on Wednesday.
In a joint statement, the WHO and the United Nations children's fund (Unicef) said it was a "momentous occasion".
"The arrival of the Covid-19 vaccines into Ghana is critical in bringing the pandemic to an end," they said.
The West African country has recorded more than 80,700 cases of coronavirus and 580 deaths since the pandemic began. These numbers are believed to fall short of the actual toll because of low levels of testing.
The WHO and Unicef said the shipment represented "part of the first wave of Covid vaccines headed to several low and middle-income countries".
So far, richer countries have been able to buy far more Covid jabs than poorer ones.
The Covax scheme was set up by the WHO, the Gavi vaccines alliance and the Coalition for Epidemic Preparedness Innovations (CEPI) to try to prevent poorer countries from being pushed to the back of the queue.
The programme is designed so that richer countries buying vaccines agree to help finance access for poorer nations, too.
It hopes to deliver more than two billion doses to people in 190 countries in less than a year. In particular, it wants to ensure 92 poorer countries will receive access to vaccines at the same time as 98 wealthier countries.
Most African countries are intended recipients of Covax, but a number of them like Senegal have been making provisions for vaccines outside the initiative.
The scheme has so far raised $6bn (£4.3bn), but says it needs at least another $2bn to meet its target for 2021.
Covax has faced some criticism for not moving quickly enough. One WHO board member, Austria's Dr Clemens Martin Auer, said it had been slow to secure vaccine deals and deliver doses to countries.
The joint statement on Wednesday said the shipment to Ghana represented "the beginning of what should be the largest vaccine procurement and supply operation in history".