Tennis Integrity Board boss Phillip Brook said: "It is vital we repair the damage and do so quickly."
Former Wimbledon champion Goran Ivanisevic said players were being hounded like "serial killers".
The joint investigation by the BBC and BuzzFeed News uncovered files showing that, over the past 10 years, 16 players who were ranked in the top 50 have been repeatedly flagged to the Tennis Integrity Unit (TIU) over suspicions their matches were targeted.
All of the players, including winners of Grand Slam titles, were allowed to continue competing.
Brook said he remained "totally confident" in the work of the TIU but said it was important that "everyone who loves our sport and watches our sport" is confident we are "doing all we can".
Chris Kermode, chairman of the Association of Tennis Professionals, added: "We are in a toxic environment for sport at the moment.
"We want to be as open and transparent as possible to demonstrate that we will look at this thoroughly. There is a zero, zero tolerance for this."
But he added: "Having lists of suspicious betting patterns do not mean corruption. They are a red flag and that is not evidence."
Ivanisevic agreed with Kermode and said he felt the allegations that tennis has failed to properly police the game were wrong.
"There is no evidence," said the 44-year-old Croat, who was Wimbledon champion in 2001.
"We are talking about algorithms and mathematics and some computer spits your name out like a serial killer and everyone is chasing you.
"Show me that somebody did something wrong - then I will believe you."
According to BBC Radio 5 live, the independent panel will "report on the effectiveness" of the anti-corruption programme and "make recommendations for change".
He added: "The panel has been asked to look into how the TIU can become more transparent without compromising the need for confidentiality.
"It will also consider additional resources for the TIU and structural changes that may enhance its independence.
"It will also examine whether the scope and reach of the tennis integrity education programme should be extended.
"The sport's governing bodies have committed to making the recommendations of the review panel publicly available and to implement them all in full."
