Former Sunderland manager O'Neill has entered a two-year contract as head coach, with the ex-Manchester United midfielder as his deputy.
The duo's first game in charge will be the friendly against Latvia on November 15.
"I'm the bad cop and he's the bad, bad cop. We're excited and I'm looking forward to it," O'Neill told ITV Sport.
Keane added: "I'm delighted and honoured Martin has asked me to work with him. I'm looking forward to working with the players and getting to the Euros."
O'Neill has been out of work since being sacked by the Black Cats last March, while Keane's last managerial post was with Ipswich Town, coming to an end in 2011.
The pair will succeed Giovanni Trapattoni, who was relieved of his duties in September following the national team's failure to make it to the World Cup finals.