This paper proposes a multidimensional flux-form semi-Lagrangian (FFSL) transport scheme for atmospheric modeling. The FFSL scheme extends one-dimensional, forward-in-time, upstream-biased, flux-form transport schemes (e.g., van Leer and piecewise parabolic method) to multidimensional cases. It is designed to handle arbitrarily long time steps and is called flux-form semi-Lagrangian (FFSL) due to its similarity to the semi-Lagrangian approach. The scheme is conservative, upstream biased, and maintains monotonicity constraints and tracer correlations, representing the physical characteristics of constituent transport. The FFSL scheme is implemented on the sphere and tested with idealized and realistic three-dimensional global transport simulations using winds from data assimilation systems. Stability is analyzed using a von Neumann approach and empirical tests on the 2D Cartesian plane. The algorithm is validated through von Neumann stability analysis, idealized experiments, and geophysical applications. The scheme is shown to be more accurate and computationally faster than existing methods, such as the van Leer scheme and fourth-order finite differences. The FFSL scheme is developed by extending 1D finite-volume schemes to multidimensional cases, with an efficient algorithm to reduce stringent time-step stability requirements. The algorithm must conserve mass without a posteriori restoration, compute fluxes based on subgrid distribution in the upwind direction, generate no new maxima or minima, preserve tracer correlations, and be computationally efficient in spherical geometry. The scheme also addresses the consistency between the tracer continuity equation and the underlying equation of continuity of the air. The FFSL scheme is tested on various 1D and 2D advection problems, including rectangular, Gaussian, wave-2, and irregular signals. The results show that the FFSL schemes (FFSL-3 and FFSL-5) perform better than the fourth-order center differencing scheme (CD4) and a standard nonconservative semi-Lagrangian advection scheme (SL3). The FFSL schemes maintain positivity of the original distribution and conserve mass exactly. Both semimonotonic and positive definite PPM maintain peaks better than the fully monotonic PPM, but at the risk of producing overshoots. The FFSL scheme is also tested on a rotating cone experiment on the x-y plane, demonstrating its stability and accuracy. The results show that the FFSL scheme can handle large Courant numbers and maintain the physical characteristics of constituent transport. The scheme is implemented on a regular latitude-longitude grid on the sphere, and the results are compared with other schemes, showing that the FFSL scheme is more accurate and computationally efficient. The scheme is shown to be unconditionally stable for nondeformational flows and has a second-order accuracy. The FFSL scheme is a general forward-in-time algorithm that can be applied to various physical problems, with the flexibility to choose the advective and flux-form operators independently.This paper proposes a multidimensional flux-form semi-Lagrangian (FFSL) transport scheme for atmospheric modeling. The FFSL scheme extends one-dimensional, forward-in-time, upstream-biased, flux-form transport schemes (e.g., van Leer and piecewise parabolic method) to multidimensional cases. It is designed to handle arbitrarily long time steps and is called flux-form semi-Lagrangian (FFSL) due to its similarity to the semi-Lagrangian approach. The scheme is conservative, upstream biased, and maintains monotonicity constraints and tracer correlations, representing the physical characteristics of constituent transport. The FFSL scheme is implemented on the sphere and tested with idealized and realistic three-dimensional global transport simulations using winds from data assimilation systems. Stability is analyzed using a von Neumann approach and empirical tests on the 2D Cartesian plane. The algorithm is validated through von Neumann stability analysis, idealized experiments, and geophysical applications. The scheme is shown to be more accurate and computationally faster than existing methods, such as the van Leer scheme and fourth-order finite differences. The FFSL scheme is developed by extending 1D finite-volume schemes to multidimensional cases, with an efficient algorithm to reduce stringent time-step stability requirements. The algorithm must conserve mass without a posteriori restoration, compute fluxes based on subgrid distribution in the upwind direction, generate no new maxima or minima, preserve tracer correlations, and be computationally efficient in spherical geometry. The scheme also addresses the consistency between the tracer continuity equation and the underlying equation of continuity of the air. The FFSL scheme is tested on various 1D and 2D advection problems, including rectangular, Gaussian, wave-2, and irregular signals. The results show that the FFSL schemes (FFSL-3 and FFSL-5) perform better than the fourth-order center differencing scheme (CD4) and a standard nonconservative semi-Lagrangian advection scheme (SL3). The FFSL schemes maintain positivity of the original distribution and conserve mass exactly. Both semimonotonic and positive definite PPM maintain peaks better than the fully monotonic PPM, but at the risk of producing overshoots. The FFSL scheme is also tested on a rotating cone experiment on the x-y plane, demonstrating its stability and accuracy. The results show that the FFSL scheme can handle large Courant numbers and maintain the physical characteristics of constituent transport. The scheme is implemented on a regular latitude-longitude grid on the sphere, and the results are compared with other schemes, showing that the FFSL scheme is more accurate and computationally efficient. The scheme is shown to be unconditionally stable for nondeformational flows and has a second-order accuracy. The FFSL scheme is a general forward-in-time algorithm that can be applied to various physical problems, with the flexibility to choose the advective and flux-form operators independently.