Horne, World Rugby's high-performance boss, will start his new role in March after nearly 14 years at the global governing body.
RA said the Australian will lead all of the country's high-performance rugby programmes, including the Wallabies, the national women's Wallaroos and rugby sevens.
He will also drive the alignment of Australian Super Rugby clubs' high-performance programmes and pathway structures with the Wallabies' systems in a bid to turn around the struggling national team.
The Wallabies crashed out of the pool phase at the World Cup in France, their worst-ever performance at the global showpiece.
Australian Nucifora, currently Ireland's high-performance chief, will take up his advisory role after the Paris Olympics.
RA will next focus on filling the Wallabies' head coach position following Eddie Jones's resignation. The governing body hopes to announce a new coach before Super Rugby starts in February.
