The independent American-style eatery will open on Bishopgate Street next month.
To celebrate the opening, it is giving away free meals to the first 100 customers from 12pm on Friday June 10.
The brand was born as a pop-up in Newcastle’s Grainger Market before it opened its first high street restaurant in 2020.
It has been a hit with diners in the North East, serving juicy cheeseburgers with premium smashed patties, homemade sauces and mouth-watering toppings.
The team have crafted a concise menu of double or triple cheeseburgers, sides, shakes and desserts.
The beef is smashed into a raging hot grill, smothered with American cheese and all the trimmings, before being steamed.
Menu highlights include the bestselling French Canadian, which comes loaded with streaky bacon, blue cheese, garlic butter, chilli-maple syrup, hash brown, American cheese and signature Stack Sauce.
The classic American West Coast Classic is simplicity at its finest with American cheese, house made Stack Sauce and shredded lettuce.
Fried chicken fiends will be all over the Turbocharger, made up of chicken tenders, baconnaise, pickled jalapenos, dry cure smoked streaky bacon, hash brown and Signature Buffalo sauce.
The sides menu includes the popular Pompeii Fries - beef dripping fries smothered with Stack Sauce, fiery ‘nduja sugo, basil oil and parmesan cheese.
The Filthy Fries combine crumbled blue cheese, Signature Buffalo and crispy onions.
Meat:Stack also serves Jersey Shakes with a range of flavour combinations, including Nutella, peanut butter and its own raspberry jam.
The Jersey soft serve ice cream comes topped with everything from Biscoff to ground coffee and maple syrup and there's a range of locally-brewed pale ales, as well as a refillable soda fountain.
“'It's finally here," Meat:Stack partner and director Allan Hyslop said.
"We are set to open our second restaurant and our first in Leeds on June 10.
"To celebrate we shall be giving away the first 100 meals free on the day from midday, so you will need to get down nice and early to grab a freebie.
"We have been overwhelmed with the welcome we have had from everyone in Leeds so far, the generosity of other local businesses and traders has been massively heart-warming.
"We look forward to developing these relationships and becoming a big part of the food scene in the city."