The 29-year-old will move in the summer after two seasons at Welford Road.
Standing at 6ft 6' and weighing over 18 stones, former Saxons skipper Skivington will fill the large void left by Irish stalwart Bob Casey, who is set to retire at the end of the season.
"Having worked with Toby Booth at Saxons level before, I know what he is about and what he expects from his players," said Skivington.
"Irish are an ambitious club with a strong coaching set-up and there are lots of talented players in the squad that I look forward to playing alongside."
Warrington-born Skivington has made over 40 appearances for Leicester, having moved to the East Midlands in 2010 after eight years at London Wasps, where he won both the Heineken Cup and Aviva Premiership.
London Irish head coach Toby Booth said: "George is a powerhouse and a very physical player who will bring additional size and strength to the front five of our forward pack.
"I already have first-hand knowledge of George, having coached him previously, and have always been impressed with his work ethic and on-field leadership.
"His experience and success means that he brings with him not only a wealth of knowledge, honesty and hard work but also a winning mentality.
"He has a lot to offer London Irish both on and off the field and I very much look forward to working with him again."
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