Quickfire extra-time goals from substitutes Ryan Jack and Scott Wright helped them beat Hearts 2-0 in the final at Hampden Park on Saturday.
Victory was the perfect response to their midweek heartache in the Europa League, when they lost the final on penalties to Eintracht Frankfurt.
Hearts survived a flurry of late chances in normal time. They had keeper Craig Gordon to thank for a remarkable save with his outstretched foot to deny Joe Aribo before Wright hit the bar.
Jack's thunderous shot from the edge of the penalty area in the 94th minute finally broke Hearts' resistance. Wright sealed the win by latching onto Ryan Kent's pass and slotting the ball past the helpless Gordon.
"It means so much, this is the cup you grow up wanting to play in and it's a dream to score in the final," Wright said.
"I'm absolutely over the moon to score and even more so to win."
Rangers manager Giovanni van Bronckhorst, who won the competition twice as a player during his three-year spell at Ibrox, capped an eventful first season in charge by guiding the club to their first Scottish Cup triumph since 2009.
"The demand at Rangers is to win trophies. It was a massive disappointment on Wednesday and it was a wee bit flat at the start but we grinded away," Jack said.
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