McKay's move to Ibrox is a done deal after Gers agreed to meet the midfielder's buyout clause in his Brisbane Roar contract.
Miller told the Scottish Sun: "Matt is a really brilliant player and I am delighted he is hopefully getting the chance to play for Rangers.
"I played beside him for two years at Brisbane and he was also my room-mate so I know him well. I get on great with the boy.
"I sold Rangers to Matt during our time together.
"He had the likes of myself, Craig Moore and Bob Malcolm all telling him all about it.
"We told him what you have to live up to as a Rangers player and what would be expected.
"That will not scare him though because he will tackle and he will work hard. He is a good player and he will do well for Rangers."