Using images from the Cassini spacecraft, we analyzed three ribbon waves in Saturn's 42°N eastward jet at 45°N, 42°N, and 39°N planetocentric latitudes. In this report, we demonstrate that the morphology, wavelength, and propagation of the ribbon waves are consistent with barotropic Rossby waves with a smaller baroclinic component. We report on the appearance and disappearance of these waves during Cassini's mission. We suggest that the temporal evolution of these waves are related to the great Saturn storm of 2010–2011. Plain Language Summary During their 1980 and 1981 flybys of Saturn, the Voyager spacecraft imaged a dark, sinuous line encircling the planet. This feature, dubbed the ribbon wave after its visual appearance, was embedded in an atmospheric jet stream at 42N latitude. The Cassini spacecraft also discovered waves in the 42N jet during its 2004–2017 Saturn mission. Using images taken by Cassini, we have identified the ribbon waves as Rossby waves, that is, planet‐scale waves that are common in atmospheres, including that of the Earth. Unlike Earth's atmospheric Rossby waves, which are only visible as undulations on weather maps, Saturn's ribbons are visually striking and may be some of the most prominent examples of Rossby waves in the Solar System. The ribbons are composed of a number of wavelengths, each of which is affected differently by the atmosphere and move at different speeds. By measuring the differing speed of these wavelength components, we compared the behavior of the ribbons to theoretical predictions for Rossby waves and estimated basic properties of the atmosphere. Because the ribbons likely extend deep into the atmosphere, they may help shed light on the how the atmosphere behaves at depths that Cassini was not able to observe directly. Key Points Cassini observed three wave‐like ribbon features in Saturn's 42N atmospheric jet from 2005 to 2014 The ribbons' morphology, mean wavelengths, and propagation are consistent with Rossby waves Their propagation places constraints on atmospheric conditions within the jet