This paper reports on a study examining the potential of reducing greenhouse gas (GHG) emissions from the building sector by substituting multi-storey steel and concrete building structures with timber structures. Life cycle assessment (LCA) is applied to compare the climate change impact (CC) of a reinforced concrete (RC) benchmark structure to the CC of an alternative timber structure for four buildings ranging from 3 to 21 storeys. The timber structures are dimensioned to meet the same load criteria as the benchmark structures. The LCA comprises three calculation approaches differing in analysis perspective, allocation methods, and modelling of biogenic CO2 and carbonation of concrete. Irrespective of the assumptions made, the timber structures cause lower CC than the RC structures. By applying attributional LCA, the timber structures are found to cause a CC that is 34-84% lower than the RC structures. The large span is due to different building heights and methodological assumptions. The CC saving per m2 floor area obtained by substituting a RC structure with a timber structure decrease slightly with building height up to 12 storeys, but increase from 12 to 21 storeys. From a consequential LCA perspective, constructing timber structures can result in avoided GHG emissions, indicated by a negative CC. Compared to the RC structures, this equal savings greater than 100%.