City councillors granted outline planning permission for shops, restaurants, cafes, a leisure centre and a new bus station.
There were 250 letters of objection, mainly about the effect on the traffic in the city centre.
Twenty five councillors were for, 13 were against and there was one abstention.
Developers TIAA Henderson Real Estate and The Crown Estate say the revamped site, due to open in 2019, will create 750 jobs.
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Some people were turned away from the extraordinary planning meeting of the city council as there was not enough space for all those who turned up.
Residents were worried about air pollution and traffic congestion, because of roads being closed as part of the plans, diverting traffic elsewhere.
There have also been concerns that the bus station will not be big enough.
Councillor Andrew Leadbetter, leader of the Conservative group on the council, said: "I'm disappointed because we believe that the development lacks ambition and is also very expensive. It's going to cost the city close to £30m which means that other things can't go ahead."
Council leader Pete Edwards, from the Labour group, said: "I'm really excited, not just for ourselves but for the citizens of Exeter.
"It's sad to see some of the opposition so vehemently against it when it's a great opportunity to go forward."
John Grinnell, deputy head of development at The Crown Estate said he was "delighted".
"This scheme would represent a substantial investment in Exeter that will support the city's position as the region's most popular destination for shopping, leisure and business, whilst boosting jobs, trade and the local economy," he said.

Hughes, 19, was born on the British overseas territory of Anguilla, but has held a British passport since birth.
"I have always known that if I was to run at the Olympics it would be in a British vest," he said.
In March 2014, Hughes broke Jamaican sprinter Yohan Blake's 100m junior record with a time of 10.12 seconds and almost beat Bolt in the 200m recently.
He was edged out at the New York Diamond League meeting in June with the Jamaican 100m and 200m Olympic champion Usain Bolt clocking a time of 20.29.
Anguillans can compete at the Commonwealth Games and World Championships, but athletes from the island are unable to enter the Olympics as Anguilla is not recognised by the International Olympic Committee.
Hughes said in 2014 that competing for Team GB "would be the best choice", something which he is now eligible for.
American Cindy Ofili (100m hurdler) has also held British nationality since birth, while compatriots Shante Little (400m hurdler) and Montene Speight (400m runner), plus Swedish-born high jumper Victoria Dronsfield, all hold British nationality.
Ofili, the younger sister of hurdler Tiffany Porter, ran a personal best of 12.60 seconds in Eugune in June - the seventh fastest time in the world this year.
However, the announcement was criticised by British athlete Richard Kilty, while former heptathlete Kelly Sotherton said she was "not sure about it".
Plans for a £70m redevelopment of Exeter bus station have been given the go-ahead.
[NEXT_CONCEPT]
Highly rated sprinter Zharnel Hughes has been ruled eligible to compete for Team GB.