Garlick has been operating as Albion's legal director-secretary since joining the club two years ago and will take over from Ashworth who is to become the FA's new director of elite development next summer.
Garlick will now work closely with Ashworth during a handover period to ensure the club are prepared for the summer transfer window.
He will be responsible for the first team, player recruitment, medical services and the academy and his appointment follows a similar pattern to that of Ashworth, who was also promoted from within in December 2007.
Club chairman Jeremy Peace said: "We decided to recruit an individual with a current working knowledge of the English game.
"Therefore we conducted an extensive search in the UK to benchmark all possible candidates to replace Dan.
"We have had Richard in mind since the start of the process and, after completing our research, he emerged as the strongest candidate.
"As with Dan when he was initially appointed five years ago, Richard already has an in-depth knowledge of the club, and a clear understanding of how we operate."
Garlick was on Rotherham United's books between the ages of 14 and 18 but after missing out on a pro contract, he opted for a career in the legal profession.
He joined Albion in May 2010, was appointed to the club board seven months later and has worked alongside Ashworth in dealing with players, their contracts and transfers.