A novel hygroscopic hydrogel with air‐stable, recyclable, and stretchable properties is demonstrated in this study. The hydrogel is prepared by the simple polymer blends of two hydrophilic polymers, poly(vinyl alcohol) (PVA) and poly(methacrylic acid) (PMAA), using ethylene glycol as a hygroscopic solvent and cross‐linker. The PVA/PMAA hydrogel is highly stretchable after absorbing water molecules from the ambient environment as plasticizers. The hydrogel shows a high mechanical strength with a Young’s modulus of 0.75 MPa, linear region of 42%, and elongation of over 550% at break, and could be hydrolyzed by water then recast for high quality film for many times. The unique advantages of this hydrogel is further demonstrated by fabricating a stretchable organic memory device using the deoxyribonucleic acid as the memory layer on top of the hydrogel substrate. The device exhibits a write‐once‐read‐many‐times type behavior with a memory ratio of 104, retention time over 105 s, and mechanical durability over 30% strain.