Electronic devices with engineered three-dimensional (3D) architectures are indispensable for frictional-force sensing, wide-field optical imaging, and flow velocity measurement. Recent advances in mechanically guided assembly established deterministic routes to 3D structures in high-performance materials, through controlled rolling/folding/buckling deformations. The resulting 3D structures are, however, mostly formed on planar substrates and cannot be transferred directly onto another curved substrate. Here, we introduce an ordered assembly strategy to allow transformation of 2D thin films into sophisticated 3D structures on diverse curved surfaces. The strategy leverages predefined mechanical loadings that deform curved elastomer substrates into flat/cylindrical configurations, followed by an additional uniaxial/biaxial prestretch to drive buckling-guided assembly. Release of predefined loadings results in an ordered assembly that can be accurately captured by mechanics modeling, as illustrated by dozens of complex 3D structures assembled on curved substrates. Demonstrated applications include tunable dipole antennas, flow sensors inside a tube, and integrated electronic systems capable of conformal integration with the heart.