Tenants of Cables Wynd House will save up to £360 per year because of the new communal device.
The 1962 housing block – known citywide as the banana flats – has had considerable problems with energy efficiency.
Some residents were paying as much as £60 per month – £720 per year – in heating bills.
The move is part of a broader redevelopment of the housing complex, which has already undergone a £1.7m revamp to install new kitchens and bathrooms to meet new government standards.
The communal boiler is the first of its kind installed by the city council, with more communal heating projects set to be rolled out in the ageing Greendykes and Wauchope House blocks later this year.
Residents will pay the council for the heating they use through a service charge along with their rent. The scheme is non-profit-making.
Nearly all of the 212 households opted to join the communal scheme rather than retain the inefficient electric storage heaters.
Resident Evelyn McCue, 67, who has lived in Cables Wynd House for 42 years, has found it a struggle to keep her home heated in recent years.
She said: “Until three weeks ago we all had storage heaters, which were such a struggle to use. They cost so much to keep going and as soon as you switched them off the room went cold, so I had heaters on in all the rooms.
“It’s even worse for me because I’m next to the lift shaft.
“It’s such a difference since we had the communal boiler. We’re all saying we’re too warm now and we’ve had the windows open lately. It’s like having a new house.”
Mrs McCue, who has lived alone since her husband passed away 11 years ago, said many families who live in Cables Wynd House are on low incomes or out of work and struggle because of the high bills.
She added: “I was paying £78 pound per month for electric and heating, most of which was heating. It’s a huge amount when you live on a pension, as well as for families on low incomes – a lot don’t work here.
“We have actually got the first three months’ heating free, but I would say I’d be saving up to £30 per month, so it will make such a difference.”
Councillor Paul Edie, the city’s housing leader, said: “The benefit of the communal heating system is that it costs much less to run than the electric storage heaters originally installed in the flats.
“This could not have come at a better time for many families as in the current economic climate some people are finding it very hard to pay their bills.
“This is all part of our ongoing commitment to help our tenants keep their homes warm and comfortable whilst keeping energy bills as low as possible.”