Jenkinson expressed his relief, stating "I'm thrilled that everything has been resolved now," during an interview with the League Two club's website.
"It's a great group of lads and it's nice to step into their environment to be honest, something I want to do is help the club from this point onwards so they can progress.
"I'll give my all to the club and the gaffer - it was a fantastic achievement for the lads to get promoted last year but the club wants to push on again now and that was a nice selling point for me."