Henrietta Knight, who plays a key role in managing the Salford businessman's equine interests, told the Racing Post the primary reason behind the decision is due to Grech spending increased time in Ireland for work purposes.
Grech had five individual horses trained in Britain last season, four with Nicky Henderson and one with David Bridgwater. Gallyhill, previously trained by Henderson, won on his second start since joining Elliott at Down Royal in May.
Knight said: "Mike is moving all his horses to Ireland because he's going to be spending more time there in the future. He's going to be working more over there, with offices in Dublin."
Knight was one of the busiest and biggest spenders during the second day of the recent Tattersalls Derby Sale, purchasing three horses for a total of €525,000, two of whom were bought for Grech at a cost of more than €200,000 each.
Brandy Love, who plundered the Grade 1 Irish Stallion Farms EBF Mares Novice Hurdle Championship Final in April, was the main flagbearer for Grech's five-strong Irish squad last season.
Knight added: "Mike had horses with Nicky Henderson last year and is very fond of him. They're great friends and it was tough for him to say he was going to move the horses across, but he feels he'd like to have them in the same country where he's going to spend most of his time so he can see them run."
I Am Maximus, who was last seen finishing fourth to Sir Gerhard in the Ballymore Novices' Hurdle at Cheltenham, is one of the most prominent horses to switch stables, while Fils D'Oudairies, runner-up at both the 2022 Aintree and Punchestown festivals for Henderson, is preparing for a tilt at the Galway festival with Elliott.
"I'd imagine Gordon, Willie and probably Gavin Cromwell will train the horses now," said Knight.
"Fils D'Oudairies is with Gordon. We're hoping he'll go to Galway for a hurdle race as Mike will be over for that. I Am Maximus is going to join Willie, and I think I Am Rocco will be heading there too."
She added: "Fortunedefortunata, who won on his first start for David Bridgwater, is also going to Gordon. A couple of the young ones we've bought at the sales will probably go to Gavin."