The 37-year-old was the Gers' leading goalscorer last season after netting 11 Scottish Premiership goals.
His contract was due to expire this month but manager Pedro Caixinha signed him up for another season.
Amoruso was at Rangers when the legendary Scot arrived at Ibrox in 2000, and the Italian finds it amazing that the evergreen striker is still "such an important" player for the Glasgow club.
“Kenny makes me feel very old! I remember when he signed for Rangers as a young guy. He was always a very good player and now he’s still going strong at the age of 37," he told The Scottish Sun.
“When I watched Rangers last season, Kenny was still a major player. He was the guy scoring big goals for the team.
“The new manager will want to bring his own players in but I was happy that he gave Kenny a contract. You need players who know what it means to play for Rangers — and that’s Kenny.
“Yes, he’s getting older now but he is still in great condition and he will be very important for Rangers during the course of this season.”
Miller has been superb for Rangers but the fact he finished top goalscorer last season was perhaps more a reflection on how poor the other striking options were than him.
Martyn Waghorn and Joe Garner - who has since joined Ipswich Town - only managed seven goals apiece and Rangers fans will be hoping that new boy Alfredo Morelos, who hit 44 goals in 59 games in Finland, will be a revelation.