Wright allegedly accepted a payment of £5,000 from undercover journalists in order to persuade the Championship clubs to sign players belonging to the "agents".
The 53-year-old was suspended from the club yesterday and now the South Yorkshire club has decided to act.
Barnsley's club statement read: "After considering Mr Wright’s response to allegations in today’s 'Daily Telegraph' about breaching FA rules over player transfers, Mr Wright was dismissed.
"The Club was unaware of such matters or involved in any wrongdoing. The Club will continue to fully investigate the issues at hand and will co-operate with the regulatory authorities as necessary".
Along with Tommy Wright, Queens Park Rangers manager Jimmy Floyd Hasselbaink and Leeds United owner Massimo Cellino were also allegedly involved in corruption cases.
The newspaper also claims that eight current and ex-Premier League managers are involved in cases of corruption.