It will be a single span concrete bridge, about 46m long and 26m wide, carrying public transport, including light rail, linking the north quay to the south quay of the Liffey.
Contractors must submit their tenders by May 15 next.
The estimated value of the contract is from €8m to €12m, the tender documents say.
The bridge has already been the subject of an Environmental Impact Statement and public consultation process.
The new bridge, just downstream of O'Connell Bridge, is part of the Transport 21 plan and will carry buses and the Luas "at this critical location across the Liffey."
"It will have cycleways and generous footpaths that will open Marlborough St and Hawkins St to greater footfall, prospective development and create a new north-south link from Abbey St to Pearse St," the city council says.
The bridge will have "an elegant contemporary design."
"It will be a slender, single span, smooth concrete structure, with the underside of the bridge being designed to be as high above the water as possible so that river traffic is not impeded."
Last Autumn, the Council said construction was due to commence in late 2009, but it is being funded under the Transport 21 programme and it is not clear if this timetable is being adhered to.
City council planners hope the bridge will open up Marlborough St and Hawkins St to prospective commercial development, creating a new hub in Dublin city centre, running from Abbey St in the north to Pearse St in the south.