The building project was awarded to Michael McNamara and Co Ltd last month.
Mallon Street Library will be six times the size of the current building, which is located on Redmond Square.
Spread over three floors, the facility will offer increased library space, as well as a research area for Wexford Studies.
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A viewing platform and windows in the building will overlook the town's historic wall, which will be conserved by the development.
Wexford Cathaoirleach Anna Fenlon said the project is "long overdue".
"In this information age it will be an important part of the educational and economic infrastructure of the county as well as the town," she said.
"People are eagerly awaiting the additional services this new library will bring."
Part-funded by the Department of the Environment, Heritage and Local Government, the Wexford County Library project will cost around €7m.
The total project will take two years and the library is expected to be open in early 2012.
(PR/KMcA)
