A total of 213 pupils, including 53 primary one youngsters, have enrolled for the new school, where lessons will be taught entirely in Gaelic.
Bun-sgoil Taobh na Pairce has been developed on the site of the old Bonnington primary school in Leith.
The school, which has 30 Gaelic-speaking staff, replaces the Gaelic medium education unit that had been based in the capital's Tollcross primary since 1982.
Alasdair Allan, minister for learning and Scotland's languages, said: "This is an exciting day as Bun-sgoil Taobh na Pairce pupils get into their new school for the first time.
"A lot of work has gone into reaching this landmark day and I would like to congratulate the staff and pupils, and wish them all the very best for the coming terms. I look forward to visiting again in September when they will have had a chance to settle in."
Councillor Paul Godzik, education convener at the City of Edinburgh Council, said: "The opening of Bun-sgoil Taobh na Pairce demonstrates the council's long-standing support for the development of the Gaelic language.
"I hope the pupils and teachers enjoy their new school, which is a really exciting development."
Councillor Deidre Brock, Gaelic spokeswoman for the authority's ruling Labour/SNP coalition, said the school was "a vitally important step forward for this indigenous language of Scotland".
Head teacher Anne MacPhail, said: "It was a real joy to see all the excited faces of the children as they came into the school for the first time today.
"The opening of the new school is a significant commitment to the future of Gaelic language in the city and I'm really looking forward to working with our pupils, staff and parents to ensure the school is a success."
A Gaelic school opened in Glasgow in 1999. It now takes pupils at both primary and secondary levels.