Mr Fleming, who was aged in his 60s, was a racehorse owner and published the Irish Racing Year Book for more than 20 years.
Established in 2003, the yearly publication has been published every year since.
A native of Co Kilkenny, he also worked as an accountant and was the owner of an accountancy firm based in Kilkenny city.
“Like everyone connected to Irish racing, I am very saddened to learn of the sudden passing of John Fleming,” Horse Racing Ireland (HRI) CEO Suzanne Eade said in a statement.
“He was a very talented and hugely respected man with a genuine passion for the sport. John had over thirty years’ experience as an accountant and advisor to many in the bloodstock industry.
“He published the Irish Racing Year Book for over two decades out of his sheer enthusiasm for racing.
“He was also a very proud racehorse owner and was on hand to greet his mare Navassas Island after she won the Listed Irish EBF Cork Stakes on Easter Sunday.
“On behalf of HRI, I wish to offer our sincere sympathies to John’s family and his many friends and associates. May he rest in peace.”
Mr Fleming died after being struck by an airport shuttle bus at Dublin Airport shortly after midnight on Thursday.
The incident took place on the Corballis Road, where he was pronounced dead at the scene.
A spokesperson for the Dublin Airport Authority (DAA) said they are “deeply addened by the tragic passing of a passenger overnight following a road traffic accident”.
“Our deepest sympathies are with the loved ones of the deceased.”
Gardaí are appealing to anyone who witnessed the incident to come forward.
Road users who may have camera footaged, including dash-cam footage and were travelling in the areas between 11.45pm on Wednesday, April 22 and 12.15am on Thursday, April 23 are asked to make this available to investigating gardaí.
Anyone with information is asked to contact Ballymun garda station on 01 666 4400, the garda confidential line on 1800 666 111, or any garda station.