The double reception was first proposed by the SDLP at the end of last year, to celebrate both teams reaching the finals of the Euro 2016 competition.
Unionists objected, saying the council had already held a civic reception for the Northern Ireland team in November.
Unionist amendments to expand the invite to other UK teams were defeated.
An amendment put forward by Ulster Unionist councillor Jim Rodgers to invite all four teams from England, Wales, Northern Ireland the Republic of Ireland was defeated by 33 votes to 20.
Unionist councillors also proposed sending letters of congratulation to all teams from the British Isles who qualified for the Euro 2016 finals, but this amendment was also voted down.
Belfast City Council has voted to invite both the Northern Ireland and Republic of Ireland football teams to a civic reception at Belfast City Hall.