The trade body for housing associations and not-for-profit landlords speaks on behalf of more than six million people.
Since joining the NHF in 2016, Moore has been its head of media, public affairs and campaigns and, more recently, director of strategic communications and campaigns.
In his new role he will manage the director of research and policy and the director of strategic communications and campaigns.
The organisation's strategic communications and campaigns department has a media team and a digital team of four apiece, a five-strong public affairs team, and a campaigns team of two. There are similar-sized teams for marketing and member communications.
The focus of the media, public affairs and campaigns team is to help secure more and better social housing.
Moore said: "It is a real privilege to represent our members at this critical time. I look forward to working with them to make the case for decent, secure social housing – to the next government and to the wider public."
In January, the NHF will launch a multimillion-pound campaign to raise awareness of, and challenge myths about, shared ownership.
Moore will start in his new role next week and report to chief executive Kate Henderson. She said Moore was appointed after a rigourous external recruitment process.
"Rhys has a passion for housing associations and an impressive record of shaping policy and building trust," Henderson added.