The amateur jockey, 37, fractured two vertebrae when his horse fell in a race at the Cheltenham Festival on 14 March.
Having had surgery in Bristol, he has been transferred to the National Spinal Unit at Mater Hospital in Dublin.
"We wish to express sincere thanks to all the personnel involved in his safe transfer," McNamara's family said in a statement.
The Irish jockey was placed in an induced coma after Galaxy Rock fell at the first fence in the Fulke Walwyn Kim Muir Challenge Cup.
He was airlifted to Frenchay Hospital, with his wife Caroline flying to Bristol the following day to be at his bedside in intensive care.
McNamara had an operation on his fractured spine, but fears that he had sustained a brain injury were allayed a week later.
The McNamara family added: "We will forever be indebted to the staff at Frenchay Hospital for the fantastic care he has received there since his injury.
"John Thomas is looking forward to the next phase of his treatment and rehabilitation in Ireland.
"We thank everyone for their ongoing support and prayers, and ask people please to continue to respect our privacy."
JT McNamara has been moved to Ireland for the next stage of his treatment after being paralysed in a fall.