The Malawian striker has penned a three-year deal with the Absa Premiership title contenders.
"We are stunned by Mhango’s pre-contract signing with Wits after having numerous discussions with him and his agent for more than a year," Tshabalala told Celtic's website.
"Even this past Friday, whilst preparing for the Kaizer Chiefs game, he adamantly denied rumours about his departure and made a commitment that he will extend his contract with us sign. I deem his conduct to be unprofessional."
Tshabalala added: "We have done everything in our power to keep Mhango but we are left with no option to let him go with immediate effect because he will no longer be 100 percent committed to the team.
"Our supporters must know we are vigorously searching for another prolific striker that will add value to the team. Yes, we still have depth but will continue beefing up the squad to the best of our ability."