McGregor finally moved on from Rangers at the end of last season after making 489 appearances for the club over two spells at Ibrox.
He won four Scottish Premiership titles, four Scottish Cups and five Scottish League Cups and is considered a club legend at Rangers.
Butland joined on a free transfer last summer and has been the outstanding first-choice goalkeeper at Ibrox.
Miller pointed out Butland has made the Rangers defence look better as there is now an implicit trust between the defenders and the goalkeeper.
He feels the greatest compliment that can be paid to the 30-year-old goalkeeper is that Rangers fans no longer talk about missing McGregor in the team.
Miller said on BBC Radio Scotland: “Just generally since he has come to the club, he has been impressive.
“The players in front of him trust him and it makes them a better defensive unit and they have a good understanding as a unit.
“It’s so vital that you have that quality of goalkeeper.
“They had many years with Allan McGregor and to take up that mantle and that’s a tribute to Allan McGregor that the new goalkeeper has come in and he has been so good that the Rangers fans don’t really talk about missing Allan McGregor because they have got an outstanding replacement.”
Butland seems re-energised in Scotland after frustrating spells at Birmingham City and Manchester United.
