We use data from the Sydney-AAO Multi-Object Integral Field Spectrograph ( SAMI ) Galaxy Survey and the Galaxy And Mass Assembly ( GAMA ) survey to investigate the spatially-resolved signatures of the environmental quenching of star formation in galaxies . Using dust-corrected measurements of the distribution of H \alpha emission we measure the radial profiles of star formation in a sample of 201 \ > star-forming galaxies covering three orders of magnitude in stellar mass ( M _ { * } ; 10 ^ { 8.1 } - 10 ^ { 10.95 } \mathrm { M } _ { \odot } ) and in 5 ^ { th } nearest neighbour local environment density ( \Sigma _ { 5 } ; 10 ^ { -1.3 } - 10 ^ { 2.1 } \mathrm { Mpc } ^ { -2 } ) . We show that star formation rate gradients in galaxies are steeper in dense ( \log _ { 10 } ( \Sigma _ { 5 } / \mathrm { Mpc ^ { 2 } } ) > 0.5 ) environments by 0.58 \pm 0.29 \mathrm { dex } \mathrm { r _ { e } } ^ { -1 } in galaxies with stellar masses in the range 10 ^ { 10 } < \mathrm { M _ { * } } / \mathrm { M _ { \odot } } < 10 ^ { 11 } and that this steepening is accompanied by a reduction in the integrated star formation rate . However , for any given stellar mass or environment density the star-formation morphology of galaxies shows large scatter . We also measure the degree to which the star formation is centrally concentrated using the unitless scale-radius ratio ( r _ { 50 ,H \alpha } / r _ { 50 ,cont } ) , which compares the extent of ongoing star formation to previous star formation . With this metric we find that the fraction of galaxies with centrally concentrated star formation increases with environment density , from \sim 5 \pm 4 \% in low-density environments ( \log _ { 10 } ( \Sigma _ { 5 } / \mathrm { Mpc ^ { 2 } } ) < 0.0 ) to 30 \pm 15 \% in the highest density environments ( \log _ { 10 } ( \Sigma _ { 5 } / \mathrm { Mpc ^ { 2 } } ) > 1.0 ) . These lines of evidence strongly suggest that with increasing local environment density the star formation in galaxies is suppressed , and that this starts in their outskirts such that quenching occurs in an outside-in fashion in dense environments and is not instantaneous .