The forward has penned a two-year deal at Prenton Park to give new manager John Barnes a boost as the Wirral outfit gear up for the forthcoming campaign.
Despite his father being sacked by Rovers at the end of last season, Moore junior was happy to extend his stay at the club.
He told Tranmere World: "I was offered a two-year deal when my father was manager here, and it was important for me to speak to the new manager and see what his plans were for me.
"I was told I'm in his plans so it was an easy decision to make. When I came to the club I thought I was going to end my career here and that my father would be manager. But it's not an ideal world. Life goes on and it's just a case of starting to play football again.
"I speak to my dad all the time and picked his brains to see what he thought. Really there was only one decision for me."