The experienced goal-getter joins the club on a two-year deal following the conclusion of his contract at Coleraine.
Allen, who has also played for Lisburn Distillery, Linfield and Glentoran, has bagged 224 goals in 517 games, and King feels his ability to find the net will be invaluable for Carrick.
“I am absolutely delighted to get Curtis in, he has been a proven goal-scorer in the Irish League for a long time now which is what we have been crying out for," he told the club website.
"Players with a track record of scoring goals are hard to find so for us to recruit a player like Curtis is massive for the Club.
"To get the signing over the line so early is very pleasing, it’s a statement of our intent and shows the type of player we are able to attract to the Club.”
Allen, who has won the Gibson Cup, Irish Cup and League Cup during his career in the Irish League, is looking forward to the new challenge.
"After coming to the end of my contract at Coleraine I have had to re-evaluate where I was personally in my own career and what I was wanting to get out of it," he said.
"The conversations I have had with Carrick have really sold the Club to me and I feel I can come here and bring lots to the team both on-and-off the pitch.
“It’s great to sign for the Club, having spoken to Stuart (King) & Peter (Clarke) I am excited to start a new chapter in my career as a Carrick Rangers player.
"I am looking forward to bringing some experience to the team and hopefully I can provide plenty of goals."