Parry presided over a winless run of 11 matches prior to his removal as boss and the club currently sit just a point above the npower League 1 relegation zone.
Moore, a former Rovers player, previously managed the club between 2006 and 2009 before leaving for Rotherham. He will take charge of Parry's backroom team of assistant manager Kevin Summerfield and first-team coach John McMahon until the end of the campaign.
Chairman Peter Johnson said: "Parting company with Les was a very difficult decision to make but we have had to act in the best interests of the club.
"I'd like to thank Les for excellent service to the club over many years. I am delighted to be able to bring a manager with the experience of Ronnie back to the club until the end of the season."
Moore added: "It's great to be back, I can't wait to get started. It's nice to have the opportunity to keep the club in League 1. I'm looking forward to being back at Prenton Park this week, meeting the players and hopefully starting things off with three points against Notts County on Tuesday night."