Shoppers will face a one-way system, hand sanitiser points, new queuing systems and shop staff wearing personal protective equipment.
Other shopping centres including Merry Hill have drawn up a similar measures to support businesses reopening.
It came as it was announced earlier this month that the fourth biggest Debenhams in the country inside the Bullring was not going to reopen.
However it is understood talks are ongoing with centre owners Hammerson and Debenhams over the future of the store.
Bosses urged customers to check which stores would be open before they visit next month.
The safety measures introduced at the Bullring and Grand Central include:
A one-way system to help customers safely navigate the centre
Clear signs re-iterating social distancing guidance and urging people to avoid shopping in large groups
Using Bullring and Grand Central Twitter, facebook and Instagram pages, digital in-mall displays and tannoy announcements to remind visitors about how to stay safe
Extra cleaning measures inside including to touch-screens
Monitoring of footfall to ensure there are not too many people in the centres at any one time
Introduction of queuing outside the centres when required to manage capacity
Installing fixed hand sanitiser stations
All customer-facing centre staff wearing protective clothing
Customers being encouraged to use contactless payment at shops.
Some restaurants will continue to be available for takeaway and delivery.
The Government is expected to issue further guidelines in the coming weeks on when these venues can reopen for dine-in customers.
The Moor Street and Centre car parks will be open but customers are advised to check online to see if the Edgbaston Street car park is open daily.
Stephanie Lacey, general manager at Bullring and Grand Central, said: “It has been a really challenging time for everyone, and we are hugely grateful to the key workers that have done so much over the past few months.
"At Bullring and Grand Central, we’re working really hard to make sure we can re-open on June 15 and that we can do so safely.
"We ask that people be patient with us though, as the way we shop is going to be different for a while, and visits might take longer than usual. We can’t wait to re-open, and to welcome back our customers.”
Mark Bourgeois, managing director UK and Ireland at Hammerson, said: “Our priority is the safety and wellbeing of all of our customers, retailers and colleagues. We have considered carefully how to create an operating environment that allows the centre and brands to reopen safely.
“Throughout our destinations we will display clear information for consumers on how to shop in this new environment, and we also have technology in place allowing us to monitor visitor numbers, to ensure there are never too many people in our spaces at any one time.”
Merry Hill revealed this week that its own measures include placing limits on the number of people and cars allowed into the centre at a time, with some parking bays closed, and other measures including one-way systems, floor stickers and staff training to ensure visitors stay socially distanced.