Keane will stay in his international position as assistant to Martin O'Neill, while also serving as Paul Lambert's assistant following the appointment.
The 42-year-old is now looking forward to what he says "promises to be an exciting challenge".
It comes after Villa's former assistant Ian Culverhouse and football operations manager Gary Karsa were suspended and then sacked for disciplinary reasons.
Lambert has hailed his new number two for his wealth of experience, both as a player and a coach.
"Although we never played together, we competed against one another and he's someone for whom I have a lot of time and respect," he added.
"He has worked under some great managers, some of the most successful in the game, and he'll be a great help to myself as well."
And Martin O'Neill has given his blessing to the dual roles his assistant will be undertaking.
"This is a good arrangement for us that allows Roy to remain in position as my assistant manager," he said.
John Delaney, chief executive of the FAI, added: "Both Martin and I have spoken to Paul Lambert and we are comfortable that this agreement will work well for us and the Irish team."