The ceremonies began with a short speech from Deputy Mayor Hamish McDouall.
"Today the No12 tram takes its first paying customers - that's you guys. So congratulations on making history," he said to the crowd of several hundred.
Paulene Emerson was asked to cut the ribbon, in honour of her late husband Martin, who was one of the driving forces behind having the tram restored.
"This was his dream," Mrs Emerson said.
"He was so devoted to the project - he even went to Australia to get parts for the tram. Martin would have been very proud if he had been here today."
Mrs Emerson and several family members were on the first trip along the waterfront.
"It brings back memories of riding the trams in Wellington."
The first passenger on the tram was Mabel Edmonds, who was born in 1912 - the same year the No12 tram was made.
As the tram pulled off with its first load of passengers, the crowd cheered and clapped.
Despite the cold weather, there was a festive atmosphere at the Tram Shed, with vintage vehicles on display.
Mr Boyd said the trust hoped it could run the tram at least one day a week.