A viable \(\:f\left(R\right)\) gravity model characterized by a sigmoid-type deformation of the Einstein-Hilbert action, aimed at explaining the observed late-time cosmic acceleration without invoking a true cosmological constant is introduced. The model takes the form \(\:f\left(R\right)=R-\mu\:{R}_{0}\left[\frac{1}{{(1+{e}^{-\gamma\:(\frac{R}{{R}_{0}}-1)})}^{\delta\:}}\right]\) where µ, R0, γ and δ are positive constants controlling the amplitude, transition scale, and slope of the modification. The proposed new sigmoid-exponential \(\:f\left(R\right)\) gravity model constructed to achieve a smooth, bounded transition from the Einstein-Hilbert regime at high curvature to an effective dark energy regime at low curvature. Motivated by phase-transition dynamics and inspired by exponential gravity forms arising in string-inspired and Gauss-Bonnet frameworks, the model ensures analytic continuity, avoids curvature singularities, and naturally yields a geometric dark energy density scaling as \(\:{\rho\:}_{DE}\propto\:{a}^{-1}\) , consistent with late-time acceleration observations. It is verified that it satisfies all key viability conditions: positivity of the first and second derivatives \(\:({f}_{R}>0,{f}_{RR}>0)\) for avoidance of Dolgov–Kawasaki instability, and a stable de Sitter attractor. The model admits a viable scalar-tensor representation with a scalar field whose effective mass depends on the ambient matter density, enabling chameleon screening in high-density environments. We demonstrate compatibility with solar system constraints, the thin-shell condition, the Compton wavelength criterion, and equivalence principle tests. Also performed a detailed phase space and statefinder analysis.
