We propose an evolutionary competition model to investigate the green transition of firms, highlighting the role of adjustment costs, dynamically adjusted transition risk, and green technology progress in this process. Firms base their decisions to adopt either green or brown technologies on relative performance. To incorporate the costs of switching to another technology into their decision-making process, we generalize the classical exponential replicator dynamics. Our global analysis reveals that increasing transition risk, e.g., by threatening to impose stricter environmental regulations, effectively incentivizes the green transition. Economic policy recommendations derived from our model further suggest maintaining high transition risk regardless of the industry's level of greenness. Subsidizing the costs of adopting green technologies can reduce the risk of a failed green transition. While advances in green technologies can amplify the effects of green policies, they do not completely eliminate the possibility of a failed green transition. Finally, evolutionary pressures favor the green transition when green technologies are profitable.