The teenager, who spent eight months in jail for causing death by careless driving in a car crash in 2012, signed a two-and-a-half year contract with Carlisle at the weekend.
His contract with Manchester City was cancelled as a result of his prison sentence, but the Cumbrians offered him a route back into the game in November when he agreed a one-month deal.
"The last couple of years have been very difficult," the forner England Under-18s captain told the club's official website.
"I've had my family to get me through it and that's been a huge help to me.
"I don't think there are enough words to describe how much I regret it.
"I wish it had never happened and I just want to say sorry for everything that did happen. If I could take it back I honestly would, with all my heart. I'm just so sorry.
"It'll be something that will be in the back of my mind every single day and I'll never forget about it. All I can do is try and move forward with my football now."
Carlisle boss Graham Kavanagh spoke of the difficult decision the club made in November when handing Meppen-Walter a fresh start.
Meppen-Walter added: "I owe a lot to Kav because he has brought me into the team and put a lot of trust in me. I just want to repay that on the pitch.
"Kav put faith in me right from the start and I didn't want it to be a case of coming here then leaving straight away."
Video footage of Meppen-Walter's fatal car accident in February 2012 was shown in a BBC Three documentary 'License to Kill'.