Rose, who joined the HCA in April 2013, will join The Global Infrastructure Investor Association (GIIA) - a global advocacy association representing equity investors in global infrastructure.
The HCA said in a statement that during his time at the agency Rose established a new investment function intended to help unlock stalled sites and increase investment in housing and infrastructure through greater use of equity and loans.
The statement also said that Rose "built up the HCA’s role as a central body within government for the disposal of surplus public land".
HCA chairman Kevin Parry said: "I would like to offer immense thanks to Andy for his highly successful stewardship of the HCA.
"Andy can be incredibly proud of the HCA’s performance during the past few years. He leaves an organisation that continues to provide new homes for thousands of people and is set to deliver the government’s recently-announced priorities for housing and public land."
Housing and planning minister Brandon Lewis also thanked Rose for his leadership at the HCA which "has led our work to deliver over 270,000 new affordable homes over the last Parliament, and to release public sector land for over 100,000 new homes."
A recruitment process to appoint a new HCA chief executive will commence shortly, the statement said.