The 29-year-old lock has spent two years with the Tigers, having previously had an eight-year stint with London Wasps.
Discussing his upcoming move, Skivington has revealed that Irish coach Toby Booth played a major role in his decision.
"Having worked with Toby Booth at Saxons level before, I know what he is about and what he expects from his players," he told the club's official website.
"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."
Skivington is a previous captain of the England Saxons.