The Colombian striker scooped the club's top goalscorer, Player of the Year and Players' Player of the Year at the event in Glasgow.
Morelos, who has struck 29 goals this season, was serenaded by Rangers fans as he picked up his trophies with boss Steven Gerrard presenting him with the Player of the Year award.
The five red cards picked up this season did little to sway votes with the player's influence in the team recognised.
The 22-year-old paid tribute to his team-mates.
He told RangersTV: "It's something incredible for me, my team-mates' support has been really important and I'm thankful for their support, both on and off the pitch, thanks to them and the whole technical team.
"I think it's unconditional, their support has been fundamental to everything that I have achieved here with Rangers.
"Without my team-mates' support one of this would have been possible. I'm thankful to all of them. Now I am going to go out and hug each and every one of them for everything, for all the support they've given me, for all the love and respect I have gotten.
"I am very happy with all of them. I'm very happy and proud they have picked me."
Meanwhile, Ryan Kent picked up the Young Player of the Year award and Ryan Jack won goal of the season for his winning strike over Celtic in the December Old Firm derby at Ibrox.
Amy Muir was the winner of the Women's Player of the Year and Josh McPake the Academy Player of the Year.
Goalkeeper Allan McGregor's efforts were recognised with the John Greig Achievement Award.