The former Brumbies hooker has been a part of Robbie Deans' back room staff since 2009 but has quit the post to pursue other opportunities.
Acting ARU Ceo Matt Carol paid tribute to Nucifora and wished him well for the future.
"David's contribution to Australian Rugby has been outstanding," said Carroll.
"Since 2008 he has led the HPU, developing new strategies and methods that have benefited and will continue to benefit rugby in Australia well into the future.
"As part of his role David has worked alongside Robbie Deans in support of the Wallabies, coached the Under-20s at the Junior World Championships and established the national Rugby Sevens program.
"David is passionate about the future of Rugby Sevens and has ensured ARU is more focused on what has to be done to achieve success in that area.
"David has also contributed significantly to the wider operation of the business, ensuring strong co-operation between HPU and other departments, in particular Community Rugby. We wish David every success in future endeavours."