He was injured at a friend's barbecue on 8 April and remains in hospital.
Jackson, 28, underwent neck surgery for what his region at the time described as a "non-rugby related injury."
"After hitting my head on the bottom I realised I couldn't swim to the surface because I'd lost movement in my legs and power in my arms," Jackson said.
Jackson, who has also played for Bath, Wasps, London Welsh and Doncaster Knights, said his father - a retired GP - and a friend realised immediately something was wrong.
They pulled him to the surface and stabilised him until the ambulance arrived to take him to Southmead Hospital in Bristol.
"After a number of MRI scans and X-Rays the Drs decided to operate at 2am to stabilise my neck as pressure was being put on my spinal cord," Jackson added in a Facebook post.
"In surgery they removed my shattered disc, relocated my vertebrae and fixed it in place with a metal plate.
"I woke up in ICU, luckily completely coherent, however no feeling below my neck other than limited movement in my right arm."
Bath-born Jackson has made 36 appearances for the Dragons since joining from Wasps in 2015 and signed a contract extension with the region in December.
Newport Gwent Dragons forward Ed Jackson has revealed he suffered a serious spinal injury after diving into the shallow end of a swimming pool.