Mr Khan was joined at the market by Marina Ahmad AM, the London Assembly member for Lambeth and Southwark.
Adrian Bunnis, chair of the market trustees, spoke about the effect of the COVID-19 pandemic on the market.
"Of course, our numbers have fallen," he said.
"But what has happened is that we've seen the return of local people to buy produce from the market.
"People have come to buy fruit, veg, meat and bread.
"We welcome that, obviously, and we'd like to cement the relationship we have with those local people.
"Of course, the market has always been a produce market. Until the late 1990s it was only a produce market. So in a way this is a return to our roots.
"What we want people to do today – because this is a produce-only market – is to come and buy good quality food produced and sourced in a sustainable fashion so that you can take it home and cook it."
In his speech Sadiq Khan noted that the market had faced plaques, fires, wars and terrorist attacks in its thousand-year history.
"Every time this market has faced those challenges it has survived and flourished and thrived as well," said the Mayor.
"I'm really proud to be here this Sunday for the first ever official Sunday opening.
"It's really important we get Londoners and visitors and tourists back to Borough Market because this is the best market in the world."
• Borough Market is open on Sundays 10am-2pm.