Seven hubs are being introduced in Wolverhampton in the first phase of the scheme, which it was first envisaged would cost £3.3 million. But costs have since swollen to £4.1m after chiefs identified extra repairs were needed.
The move will save £1m a year in utilities bills for buildings which have since closed and in staff costs.
Now it has been revealed work will start in September on the first hub of the project, Ashmore Park, which won planning permission to go-ahead last week.
Interested parties are meanwhile being invited to tender for work on the Wednesfield, Long Knowle, Pendeford and Parkfield hubs.
Two further hubs are also included in the first phase at Lower Bradley and Low Hill. Designs, led by community design groups, are at an early stage in both cases but tenders for Low Hill will be invited in the coming weeks.
Construction has been phased so residents of areas across the city will retain library services near their home as the project takes shape.
Tenders are meanwhile running separately for each hub, so council bosses can achieve the best value for money from the most suitable specialist firm for each.
Councillor Elias Mattu, the city council's leisure boss, said: "We're doing this because we want to give our communities the best possible buildings they can have.
"We're doing repairs and improvements as we go along because we want these buildings to be in place for the next 25 years."
When plans were first unveiled they sparked controversy from critics who said they would 'rip the hearts out of communities' as library buildings closed.
Council chiefs however said the project provided a guarantee no library services would be lost across the city, in stark contrast to other councils across the country.
Councillor Mattu added: "One of the most difficult challenges with cuts is to be innovative and creative in the way we protect and safeguard services.
"This scheme is unique as it saves our libraries. People were skeptical at first but I now have people who petitioned against it telling me that it is actually a good idea."
It comes as Collingwood Library is due to relocate from a shop on The Broadway, Bushbury, to Broadways Gardens, the ExtraCare retirement centre, around 300ft away.
Thousands of people signed petitions objecting to original plans, forcing council bosses to drop some of their original proposals.
But it is ploughing forward with plans to move Warstones, Spring Vale, Ashmore Park and Collingwood Libraries.
Warstones Library is to move to Warstones Resource Centre. Spring Vale Library is going from its site in Hateley Drive to the former Parkfield High School.
Penn Library was saved from the axe following a campaign launched by users.