Morgan has hosted the station's flagship weeknight programme, Piers Morgan Uncensored, since the channel launched at the end of April but will now take an extended summer holiday before returning in September.
In his stead, Kyle will take the reins ahead of his own new show launching on the channel this autumn.
"I can imagine no finer broadcaster to keep my seat warm," said Morgan. "Well, I can, but they weren't available. I'm sure he'll do his best."
Kyle, who also hosts Drivetime on talkRADIO, said: "It is an honour and a privilege to take the helm on Uncensored while Piers is away.
"He is the pre-eminent broadcaster of his generation. At least that's what he told me to say.
"I'm looking forward to keeping his audiences in the UK, US, Australia and beyond informed, entertained and engaged with the best guests, the most challenging interviews and plenty of fun."
During his break Morgan will also film a new series of his true crime documentaries. body check tags ::