The 35-year-old has assumed control at The Jakemans Stadium with immediate effect following a successful spell in charge of Football League side Mansfield Town.
United chairman David Newton told bufc.co.uk: "We went through a thorough process to find the right person for the job and we are delighted to unveil Adam as our new first team manager.
"Adam was the outstanding candidate and certainly impressed during the interview process.
"Despite being relatively young in managerial terms, Adam has impressed at Mansfield Town and we are extremely pleased to have him onboard.
"He will get started straight away in a bid to engineer a climb up the table and we will give him every support possible."
Stay tuned for more Adam Murray coverage over the weekend.