Modern wheat cultivars are increasingly sensitive to ground level ozone, with 7–10% mean yield reductions in the northern hemisphere. In this study, three of the genome donors of bread wheat, Triticum urartu (AA), T. dicoccoides (AABB), and Aegilops tauschii (DD) along with a modern wheat cultivar (T. aestivum ‘Skyfall’), a 1970s cultivar (T. aestivum ‘Maris Dove’), and a line of primary Synthetic Hexaploid Wheat were grown in 6 L pots of sandy loam soil in solardomes (Bangor, North Wales) and exposed to low (30 ppb), medium (55 ppb), and high (110 ppb) levels of ozone over 3 months. Measurements were made at harvest of shoot biomass and grain yield. Ae. tauschii appeared ozone tolerant with no significant effects of ozone on shoot biomass, seed head biomass, or 1000 grain + husk weight even under high ozone levels. In comparison, T. urartu had a significant reduction in 1000 grain + husk weight, especially under high ozone (−26%). The older cultivar, ‘Maris Dove’, had a significant reduction in seed head biomass (−9%) and 1000 grain weight (−11%) but was less sensitive than the more recent cultivar ‘Skyfall’, which had a highly significant reduction in its seed head biomass (−21%) and 1000 grain weight (−27%) under high ozone. Notably, the line of primary Synthetic Hexaploid Wheat was ozone tolerant, with no effect on total seed head biomass (−1%) and only a 5% reduction in 1000 grain weight under high ozone levels. The potential use of synthetic wheat in breeding ozone tolerant wheat is discussed