The gunman then fled in a silver van with Northern Ireland number plates.
The club was where Taylor - Ireland's Olympic, European and World champion - began her career, before going on to win gold at London 2012. The gym was established by Mr Taylor.
Pete Taylor, 57, suffered serious but not life-threatening injuries.
A 50-year-old man was killed and another man, aged 35, was injured, Irish police said, in an attack which came "out of the blue".
"There were about 15-20 people in the gym". They were not aware of any pre-existing threats to any gym member.
After viewing CCTV in the area, Gardaí have appealed for information on a silver coloured Volkswagen Caddy with Northern Irish plates which is believed to be the getaway auto.
It happened at Bray Boxing Club shortly before 7 o'clock this morning.
Gardai said the body of the man remains at the scene pending the arrival of the State Pathologist.
Fellow councillor Michael O'Connor added: "Pete Taylor was shot".
Lines of gardai searched the harbour at Bray as they launched a manhunt for the killer.
Bray Municipal Council chair Chris Fox said: "Bobby would be very well-known in sporting circles in Bray, very much into soccer and keeping fit and used to go to the club before his day's work".