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Abstract Rapidly controlling and switching adhesion is necessary for applications in robotic gripping and locomotion, pick and place operations, and transfer printing. However, switchable adhesives often display a binary response (on or off) with a narrow adhesion range, lack post‐fabrication adhesion tunability, or switch slowly due to diffusion‐controlled processes. Here, pneumatically controlled shape and rigidity tuning is coupled to rapidly switch adhesion (≈0.1 s) across a wide range of programmable adhesion forces with measured switching ratios as high as 1300x. The switchable adhesion system introduces an active polydimethylsiloxane membrane supported on a compliant, foam foundation with pressure‐tunable rigidity where positive and negative pneumatic pressure synergistically control contact stiffness and geometry to activate and release adhesion. Energy‐based modeling and finite element computation demonstrate that high adhesion is achieved through a pressure‐dependent, nonlinear stiffness of the foundation, while an inflated shape at positive pressures enables easy release. This approach enables adhesion‐based gripping and material assembly, which is utilized to pick‐and‐release common objects, rough and porous materials, and arrays of elements with a greater than 14 000xrange in mass. The robust assembly of diverse components (rigid, soft, flexible) is then demonstrated to create a soft and stretchable electronic device.