The 57-year-old will fill the gap left by Giovanni Trapattoni's departure at the start of September following a string of poor results while the search for a permanent replacement continues.
Ireland's FIFA World Cup qualification hopes were effectively ended by consecutive defeats against Sweden and Austria earlier this month, and the Italian manager's five-year reign came to an end by mutual consent.
They face two more qualifiers in October, away to group leaders Germany and at home to Kazakhstan.
The FAI confirmed that Ray Houghton and Ruud Dokter would "carry out a comprehensive assessment of (the) market" to find a new boss ahead of the UEFA Euro 2016 qualifying campaign.
King took charge of the Under-21s in 2010 and has guided them to a number of good results this year, including a 3-0 win over Holland in February.
