Integrated optical modulators with high modulation speed, small footprint and large optical bandwidth are poised to be the enabling devices for on-chip optical interconnects. Semiconductor modulators have therefore been heavily researched over the past few years. However, the device footprint of silicon-based modulators is of the order of millimetres, owing to its weak electro-optical properties. Germanium and compound semiconductors, on the other hand, face the major challenge of integration with existing silicon electronics and photonics platforms. Integrating silicon modulators with high-quality-factor optical resonators increases the modulation strength, but these devices suffer from intrinsic narrow bandwidth and require sophisticated optical design; they also have stringent fabrication requirements and limited temperature tolerances. Finding a complementary metal-oxide-semiconductor (CMOS)-compatible material with adequate modulation speed and strength has therefore become a task of not only scientific interest, but also industrial importance. Here we experimentally demonstrate a broadband, high-speed, waveguide-integrated electroabsorption modulator based on monolayer graphene. By electrically tuning the Fermi level of the graphene sheet, we demonstrate modulation of the guided light at frequencies over 1 GHz, together with a broad operation spectrum that ranges from 1.35 to 1.6 µm under ambient conditions. The high modulation efficiency of graphene results in an active device area of merely 25 µm(2), which is among the smallest to date. This graphene-based optical modulation mechanism, with combined advantages of compact footprint, low operation voltage and ultrafast modulation speed across a broad range of wavelengths, can enable novel architectures for on-chip optical communications.