The challenge centred on the most contentious aspect of the act which offered conditional immunity to suspects in exchange for information about Troubles-related crimes.
Government lawyers had argued in an appeal hearing last month to retain the immunity provision.
Senior judges at the Court of Appeal were expected to give their ruling in the case this autumn.
But now the new Labour government has abandoned that appeal in keeping with its pledge to scrap and replace the Troubles Legacy Act.
The move was confirmed in a written Westminster statement by North of Ireland Secretary of State Hilary Benn.
He said the government had written to the Northern Ireland Court of Appeal to “formally abandon all its ground of appeal” against the provisions around immunity from prosecution.
“This is the first step in fulfilling the government’s manifesto commitment to repeal and replace the act,” he added.
He accused the previous Conservative government of ignoring the views of victims and survivors.
“The conditional immunity provisions in particular have been opposed by all of the Northern Ireland political parties and by many victims and survivors, as well as being found by the court to be unlawful,” he said.
The Secretary of State also confirmed plans to remove the “offending provisions from the statute book”.
Mr Benn defended his decision to retain another key element of the act – the Independent Commission for Reconciliation and Information Recovery (ICRIR).
He said the courts had found the commission to be independent and capable of conducting human rights compliant investigations.