Last month, planners recommended the council should reject the proposal.
The units which Lidl pursued only have planning permission for the sale of bulky goods, like furniture.
The planners said changing the use would conflict with policies which favour the use of existing suitable sites.
Last year, the future viability of the shopping centre was called into question when both Tesco and Dunnes Stores pulled out of it.
Alliance councillor David Armitage, who abstained from voting so that he could speak in favour of approving the plan, said the right decision was reached.
"I'm absolutely delighted the initial decision to decline Lidl has been overturned," he said.
"While some still saw fit to argue against the application, hopefully the years of struggling for Connswater are now over and the local community can look forward a revived period for the centre."
However, the Green Party's Ross Brown said the approval leaves the council open to a potential legal challenge that could prove costly.
"I'm not at all against Lidl and in fact I think it would be a good addition to the area, but this opens the door for a judicial review by Tesco and ultimately it's the ratepayers who have to shoulder the cost if that happens," he said.
Belfast City Council has backed a plan to open a new Lidl store at Connswater retail park in east Belfast.