Captain Keane missed Friday night's 6-1 drubbing by Germany with an Achilles injury, but has trained with the team for the last two days and comes in to partner Jonathan Walters up front.
He is one of three changes to the team that was mauled by the Germans as embattled boss Giovanni Trapattoni reverts back to his favoured 4-4-2 formational.
Manchester United youngster Brady is handed his first competitive start and is likely to play on the right wing with Aiden McGeady moving to the left.
Keith Fahey and Simon Cox are the two men who played in midfielder against the Germans who miss out.
The only other change sees Stoke defender Marc Wilson replace Stephen Ward at left-back.
Trapattoni is in desperate need of a win with one Irish bookmaker having already suspended betting that he will still be in the job by the end of the year.
Republic of Ireland team to play Faroes Islands: Westwood; Coleman, O'Shea, O'Dea, Wilson; Brady, Andrews, McCarthy, McGeady; Keane, Walters