Liverpool-born Barry (34) will stay with Chelsea and join Kenny's staff on a part-time basis.
He is a highly-regarded operator who was at Everton in his youth but quit playing early to concentrate on forging a career in the coaching sphere.
Frank Lampard appointed Barry to his Chelsea staff last summer off the back of a three-year spell where he assisted former Sligo Rovers boss Paul Cook at Wigan Athletic.
Barry has retained his job at Chelsea despite the exit of Lampard to make way for Thomas Tuchel and recently turned down the manager's job at Fleetwood Town.
"The opportunity to work in international football is something I'm thoroughly looking forward to and I'm looking forward to working with manager Stephen Kenny, his staff and the squad. I'd also like to thank Chelsea for helping facilitate this opportunity," said Barry in an FAI statement.