Although it was officially opened yesterday by Lord Mayor, Emer Costello, motorists were finally able to avail of the added convenience of the bridge at 7am this morning.
It is expected the alternative route across the city will bring welcome relief for drivers facing traffic congestion on the clogged-up city centre.
It has four traffic lanes, cycle tracks and footpaths and has the capacity to be used by bus and light rail services in the future.
The new structure, which took seven days to travel from Rotterdam to Dublin, links Guild Street on the northside with Sir John Rogerson's quay on the south.
Yesterday's opening ceremony was attended by Nobel Prize winner Seamus Heaney as well as Beckett's niece and nephew, Caroline Murphy and Edward Beckett.