Analyzing how climate change has affected forest growth is crucial for predicting future dynamics and adapting forest management to future climate change. In this paper, we investigate how climate change has modified stand dominant height dynamics and site index of 20 European tree species. We used an innovative method based on an annual height increment equation to model stand dominant height as a function of climate back to 1872 and of other stand environmental conditions. We used these models to simulate stand dominant height dynamics and site index under two different climates (prior to climate change and actual recent climate) to analyze the impact of climate change over the past century. To build our models, we combined the recently published FYRE long-term climate database, which provides daily data since 1871, with data from more than 17,000 forest stands of the French National Forest Inventory network. Higher temperature, precipitation and climatic water balance generally favor stand dominant height dynamics when the variables are considered separately. However, the positive effects often saturate at the higher end of the variable distribution. Over the past century, the effect of climate change on the site index has varied widely among species, ranging from a decrease of less than 3% to an increase of more than 5%. The effect of climate change has also varied within species, with more positive effects on initially temperature-limited stands for some species. For the species and environmental conditions considered, our results highlight a positive response of site index to past climate change for most species, albeit with between- and within-species differences. Our results also suggest that this positive response could become negative under continued climate change. These conclusions, as well as the quantitative relationships we provide between climate and stand dominant height dynamics or site index, will help design management strategies to adapt forests to climate change.