Climate policy objectives require zero emissions across all sectors including steelmaking. The fundamental process changes needed for reaching this target are yet relatively unexplored. In this paper, we propose and assess a potential design for a fossil-free steelmaking process based on direct reduction of iron ore with hydrogen. We show that hydrogen direct reduction steelmaking needs 3.48 MWh of electricity per tonne of liquid steel, mainly for the electrolyser hydrogen production. If renewable electricity is used the process will have essentially zero emissions. Total production costs are in the range of 361–640 EUR per tonne of steel, and are highly sensitive to the electricity price and the amount of scrap used. Hydrogen direct reduction becomes cost competitive with an integrated steel plant at a carbon price of 34–68 EUR per tonne CO2 and electricity costs of 40 EUR/MWh. A key feature of the process is flexibility in production and electricity demand, which allows for grid balancing through storage of hydrogen and hot-briquetted iron, or variations in the share of scrap used. •A process design for hydrogen direct reduction (H-DR) steelmaking is proposed.•3.48 MWh electricity are consumed per ton of steel product.•H-DR emits only 2.8% of blast furnace CO2.•Competitive production cost at low electricity and moderate carbon prices.•High flexibility due to hydrogen and HBI storage, and varying scrap charge.