Palmer linked up with Rovers on a six-month deal from Sheffield Wednesday this week.
"All you want to do as a player and young lad is play football and I'm thankful for Tranmere for giving me that opportunity and I can't wait for the season to get under way," he told the club's official website. "I need to get a good run of games to get experience and learn my trade. It would be good to get 20-25 games up until Christmas and take it from there.
"Everyone has made me feel welcome at Tranmere and both Sheffield Wednesday and Tranmere fans have been writing to me on Twitter wishing me well. I want to get used to playing Saturday-Tuesday and hopefully play well during my time here."
Rovers boss Ronnie Moore said Palmer's versatility was a factor in his pursuit of the player, and the 20-year-old is content to play wherever selected.
He added: "I've always said that as long as I'm playing I'm happy and I'll give 100% in any position. It gives me more of an opportunity of playing if I can play in more than one position."