The planned memorial, entitled "Memory Wound", would have seen a wide slit cut into a strip of land near the island of Utøya where most of Breivik's 77 victims were killed.
The project was generally approved of aesthetically, but about 20 locals, some of whom helped save lives during the massacre, sued the state to block the project, arguing it would harm the local community and landscape.
They saw the planned memorial as too invasive and too close to their homes.
In order to appease critics, Norway's Minister of Communal Affairs and Modernisation, Jan Tore Sanner, said Wednesday the project would be abandoned, and another as-yet undecided memorial would be raised on the dock where the ferry to Utøya departs.
"We have several years of debate behind us about where to place the national memorial," Sanner told a press conference.
"We hope to now be able to put a dignified end to this debate."
While the government's decision puts an end to the lawsuit, it is not certain that all of the locals will approve of the new project.
"Think of the people who will now have a memorial in their backyard," the lawyer for some of the ex-plaintiffs, Harald Stabell, told AFP.
"Imagine living with a memorial every day, when they themselves helped save some of the youngsters," he said.
Utøya was the scene of Breivik's gun rampage on July 22nd, 2011.
Disguised as a policeman, he spent more than an hour shooting at hundreds of people, most of them teenagers, gathered for a summer camp organised by the Labour Party's youth wing, killing 69 of them.
He had earlier killed eight others by blowing up a bomb outside a government building in Oslo.
The 38-year-old right-wing extremist, who recently changed his name to Fjotolf Hansen, is serving a 21-year prison sentence that can be extended indefinitely.