Councillors have approved plans for a community-owned "mutual" that would be commissioned by Devon County Council to run the service on its behalf.
In February, the authority approved £46m of cuts for 2015-16 after a drop in government funding.
But union Unison warned that job posts and libraries could still close.
Andy Bowman, from the union, which represents library staff, said: "The authority could cut back the amount of money it pays for the 'mutual' library service, forcing it to cutback on the number of libraries and staff.
"It's abdicating its responsibility to this new body and distancing itself from the bottom line decisions as to who has jobs and what libraries stay."
However, the Conservative-led council said that in response to "overwhelming support" from communities who wanted to work more closely with the libraries, the new organisation would "continue to deliver an affordable, sustainable and innovative library service".
Conservative councillor Roger Croad, cabinet member with responsibility for the library service, said: "We have seen library closures happening across the country, and we want to avoid that happening here."
The authority has cut £3m from its library service budget over the past three years.
Devon's entire library service is to be turned into an independent organisation in a bid to save £1.5m over the next two years.