The former Manchester United and Republic of Ireland midfielder has signed a two-year contract with the English Championship side, who sacked former boss Jim Magilton on Wednesday.
The 37-year-old has been out of work since departing as Sunderland manager last December.
Keane told the club's official website: "I truly believe that I am joining a club that has the potential, ambition and infrastructure to once again be a Premier League side.
"The club's owner (Marcus Evans) and chief executive (Simon Clegg) impressed upon me their total focus on achieving this quest at the earliest opportunity and I can't wait to get started."
Magilton fell as a victim to the Portman Road regime's top-flight aspirations on Wednesday when he was sacked as Ipswich manager after failing to lead them into the Championship play-offs.