The 21-year-old right-handed shot most recently played for Solihull Barons in NIHL 1 League and is known for his high energy pressure style of play.
Mulcahy scored a point a game for the Barons last season, winning their young player of the year award, and will be stepping up to National League level for the first time.
Head coach Tom Watkins said: “I think this guy will turn a lot of heads this season.
“Not a lot of people will be aware of him or what he will bring to the table but watching him it’s clear he’s a good skater, has a tremendous work ethic and decent skill set but from a coaching point of view he does the little things to a high standard, takes pride in that side of his game and I don’t think you can put a value on that.
“I believe he will be a reliable, consistent performer for us. I also believe he will be a pain in the backside to play against, a guy who has a team first attitude and will do whatever it takes to help the team.
“I think Dan will thrive in our dressing room and at this level. I’m looking forward to working with him.”
Mulachy added: “I am excited to have been given the opportunity by Tom to step up a league and I know Telford will be the perfect club to continue improving with the vast experience of Tom and the core group of players.
“I’ve heard great things about the fans and the squad so I can’t wait for the season to get going.
“It will be a privilege to play for such a successful team and hopefully I can help to continue the run of silverware and success of recent years.”