The agricultural sector can contribute to climate change mitigation by reducing its own greenhouse gas (GHG) emissions and sequestering atmospheric carbon in vegetation and soils, and by providing biomass for substituting fossil fuels and other GHG intensive products in the energy, industry and transport sectors. New policies at EU level provide incentives for more sustainable land use practices, for example, cultivation systems using perennial plants that provide biomass for food, bioenergy and other biobased products along with land carbon sequestration and other environmental benefits. Based on spatial modelling across more than 81,000 landscapes in Europe, we find that introduction of grass-clover leys into rotations with annual crops could result in soil organic carbon sequestration corresponding to 5-10% of total current GHG emissions from agriculture in EU27+UK, annually until 2050. The combined annual GHG savings from soil carbon sequestration and use of biogas produced in connection to grass-based biorefineries equals 13-48% of current GHG emissions from agriculture. The assessed environmental co-benefits (reduced wind and water erosion, reduced nitrogen emissions to water, and mitigation of impacts associated with flooding) are considerable. Besides policy instruments, new markets for grass biomass, e.g., as feedstock for producing biofuels and protein concentrate, can incentivize widespread deployment of in-rotation grass cultivation.