The former Ireland captain, who quit as manager of Premier League strugglers Sunderland in December, takes over two matches from the end of the season with the East Anglian side in ninth place and unable to qualify for the promotion playoffs.
Jim Magilton was sacked by Ipswich on Wednesday.
"He (Keane) has extensive contacts in the game and is a proven winner who encourages his team to play the attractive football that Ipswich fans have come to expect," owner Marcus Evans told the club's website.
"I believe he is the right man to take this club where we want to be, the Premier League."
Keane said he realised three or four weeks after leaving Sunderland that he wanted to get back into management.
"If I wasn't up for the challenge I would be at home today walking the dogs, and the dogs needed a break," Keane told a news conference.
"I thought if the right challenge came up I was ready for it. It was a gut feeling because of the ambition of the club, the history of the club. I am lucky to get this opportunity and I'm really looking forward to it.
"The club's owner and chief executive impressed upon me their total focus on achieving (Premier League status) at the earliest opportunity and I can't wait to get started."
Ipswich were last in the top-flight in season 2001-02.
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