Hibernian's 20,421-capacity stadium will host the game on April 6 with the match being screened live by BBC Alba.
With Hampden being unavailable because of redevelopment work for the Commonwealth Games, there had been much debate about where the game should be played.
Ally McCoist's side reached the final after Jon Daly's goal secured a 1-0 victory over Stenhousemuir in Tuesday night's semi-final at Ochilview.
And skipper Lee McCulloch believes reaching their first final since Rangers went into administration and liquidation last year shows they are on the right track on their road to recovery.
Rangers fans last savoured a final in more high-profile fashion as their team won the League Cup against Celtic at Hampden in 2011.
This competition may be contested by Scottish football's lower league sides but McCulloch was keen to emphasise the importance of the cup to Rangers.
He said: "It means the world to us. This is the first final this group of players has got to. It means so much to us.
"It's a chance to go and lift a cup and to show everybody that the club is progressing and getting back to where we should be."
The last-four clash against Stenhousemuir was not quite as convincing as the 8-0 thrashing handed out by Rangers when the sides met in the league at Ibrox last month.
McCulloch said: "I thought we dominated the game. We hit the bar twice in the first half, created a few other chances, and I didn't think they really looked like scoring.
"We just had to be patient and, finally, we got there in the end with big Jon's brave header and we saw the game out."
And the Gers skipper was delighted to make amends for last year's exit on penalties to eventual winners Queen of the South.
He said: "We spoke about that before the game. We remembered how we felt last season when we got put out on penalties.
"We are just delighted to have pushed on from last season and got to a final.
"The final is six months away, which is a bit of a strange one, so it's just all about getting points on the board in the league just now and looking forward to the final."