The centre, which opened in September, has been bought by Hammerson, co-owners of the Bullring shopping centre, also in the city.
Hammerson CEO David Atkins described Grand Central as a "highly-prized trophy" and said the firm was a strong supporter of the city and its future.
Contracts have been exchanged with Birmingham City Council, he said.
Council leader John Clancy said he was delighted Hammerson shared the council's vision for the city.
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The council said it bought the old Pallasades centre, where Grand Central is now based, in 2008 for £90m, always with the intention of selling it.
It was bought in order to allow the Grand Central development to go ahead.
The centre, which has John Lewis as its flagship store, has performed strongly since opening, Hammerson said, attracting an average footfall of 62,000 per day in its first three months of trading.
This rose to 105,000 per day over the Christmas period, with many retailers trading well ahead of budget since opening, the firm added.
Grand Central, the new shopping centre above Birmingham New Street station, has been sold for £335m.