The deal overcomes a split in cabinet over the 13 billion euros (USD 15 billion) plus interest that the EU says Apple owes in back taxes, putting Ireland at the centre of a row between Europe and the United States.
Apple chief Tim Cook has urged the government to appeal the ruling to secure future investments but opinion polls have shown public support for Ireland taking the money and spending it on social services.
Parliament will meet next Wednesday, ahead of its scheduled return on September 27, officials said.
Earlier this week, three independent ministers propping up the government had refused to back the appeal and said they wanted greater transparency about corporate tax arrangements for multinationals.
More From This Section
But after the cabinet meeting, Shane Ross of the Independent Alliance said he and his colleague Finian McGrath had supported the government position.
"We felt there was a state of urgency because there was uncertainty out there in the markets amongst some multinationals," he said.
Katherine Zappone, another dissenting independent, confirmed she too had agreed to the appeal "in the public interest".
The back taxes that the European Commission has determined the US tech giant owes are equivalent to around five percent of Ireland's gross domestic product and almost all of its annual health budget.
"Ireland is caught in a dispute between the EU and US over which it has little control," the UK-based Financial Times newspaper wrote in an editorial.
"Bowing to the commission's ruling would... Be a tacit acknowledgement that there has indeed been something rotten in the low-tax regime that Dublin operates to attract multinationals," it said.