Kenna will take immediate charge and has been given a three-year term as manager of Galway United.
A former captain of Blackburn Rovers, Derby County and Birmingham City and a Premiership winner with Blackburn.Billy Clery, who has served as caretaker manager for the past few weeks, has been appointed assistant manager.
Kenna said he is excited about the challenge ahead.
"I have been trying to get into the coaching and management side of things for the last season. I am delighted and thrilled to be given this opportunity to work with the board and Galway United. There are some good young lads coming through. Hopefully I can add something to that and that can only benefit the club."
Galway United chairman John Fallon said: "Jeff is a proven leader of men. You have here a man who is prepared to back himself. That is what Galway United needs. The board has decided and will find the resources to strengthen the squad and that will be done at the earliest opportunity."
Galway United Chief Executive Nick Leeson said: This will signal a change of direction for the football club. We wanted a fresh approach, but not necessarily somebody steeped in League of Ireland tradition. I'm excited by the prospect of working with Jeff, as are the remainder of the board. Our season, I believe starts now," he said.