With his 14 goals in Europa League qualifying and group stages, the Colombian sits top of the historic scoring charts.
Morelos has been crucial in helping the team not only reach the group from the first qualifying round but also knockout stages.
The striker paid tribute to his team-mates and said it has always been a dream to score goals.
“It is amazing to find out that I have broken this record, but of course it wouldn’t be possible without all of my teammates helping me," he told the Rangers website.
“To score for Rangers is always really meaningful to me and I enjoy scoring for the fans every single time. I love playing in big European matches here and to be able to set this record is a proud moment.
“I always dreamed about scoring in in really competitive leagues and competitions when I was a kid.
“I know that I have to keep growing and doing things right in every match, which I know I will with the support of my teammates and coaches here at Rangers.”
Rangers boss Steven Gerrard paid his own tribute.
“Alfredo has been in fantastic form for us both in the league and especially in the Europa League," he said.
“To be so close to taking the overall record for scoring in the Europa League from his countryman and idol Falcao is a real achievement and we congratulate him for all his efforts so far this season.”