Your body’s cells are not actually replaced every seven years.

For example, neurons are amitotic, or they do not undergo the process of cell division. They are in your body throughout your entire life, and you do not get new neurons once they die. Muscle cells also do not divide.
Your entire body is not made of cells.
The tattoo is put in a part of your skin called the dermis. The dermis is directly below the epidermis, or the part of your skin that is on the outside. The epidermis is the part of your skin that sheds. The dermis, however, is made of dense irregular connective tissue, and is what gives your skin that stretchy-elastic component. All connective tissue has an extracellular matrix (ECM), or a substance that surrounds the cells inside it. Dense irregular connective tissue is full of collagen, a protein, which runs in all directions so your skin will not rip. Inside the collagen fibers are cells called fibroblasts, which make the collagen, and the amount of collagen greatly surpasses the amount of fibroblasts. The ink of the tattoo lasts so long because it is in the fibers, or ECM, not the cells.