Carpentry and Woodworking - Securing a cabinet to the wall

I have 2 cabinets that I am stacking one on top of the other in an alcove and need to secure them to the wall. I am using them as a kitchen pantry. The problem is that in order to be flush to the front of the wall (which is the look I want) they are about 2 1/2 inches from the back wall. What is the best way to secure them to the back wall. I have seen some 'cleats' used by bevelling a piece of wood whereby the top of the cleat sits snugly on the bottom cleat. Unfortnately the wall is not square and I don't have any fancy tools to plane the cleat to be flush. Any suggestions would be greatly appreciated. :confused:

I would start with at least 2 studs (2x4 material) mounted vertically and flat on the back wall. That gives you a base to secure each cabinet to each stud as long as you stay within the 3.5" width of the stud. It also gives you approximately 1" of depth remaining.

Next, mount a 1x4 horizontally on the back of each cabinet. That should soak up another 3/4" of the depth. Finally, drive four (4) 3" screws through the back of the cabinet; through the 1x4 and into the studs. Hold the cabinet in place until all the screws are driven so that the alignment of the cabinet face is where you want it.

Since you are using this as a pantry, consider driving additional screws into each 3.5" x 3.5" intersection of the 1x4 with the stud for additional holding power.