These services will now be run as a not-for-profit 'mutual' as part of the authority's drive to save cash in the wake of Government cuts.
All libraries, library links and the archive service will remain open, with the new combined service less reliant on council funding, which means a council saving of 11 per cent in 2016-17 rising to 30 per cent by 2017-18.
Councillors unanimously waved through the plans at a meeting on Monday.
Councillor Rachel Harris, cabinet member for health and wellbeing, said the mutual scheme marked 'a new era' for the borough.
She told the full council meeting : "This is an absolutely historic occasion for this council.
"It marks the end of a very long and hard journey.
"It's the start of a new journey and a new era which I'm positive will be a solution for keeping a vibrant libraries and archive services here in Dudley.
"This happens in the face of rapidly decreasing resources.
"We are becoming an exception in Dudley, as councils across the country are cutting back further and further."
The libraries and archives service will continue to be run by professional staff, but have community, employee and council involvement at board level.