When ocean crust interacts with seawater at low temperatures it can form carbonate minerals that trap carbon—a process that contributes to Earth's long-term climate evolution. We studied how and when this process happens by dating carbonate veins in ocean crust from different ages and locations. Our results show that in older (Mesozoic) crust, carbonate formed quickly after the crust was created, while in younger (Cenozoic) crust, it took longer to form. We also found that carbonate formation can continue for a long time in areas where the crust is more exposed. Using models, we show that past ocean conditions—such as warmer temperatures and different seawater chemistry—made it easier for carbonates to form in older crust. This helps explain why older crust contains more carbonate than geologically young crust and plays a bigger role in storing carbon over long timescales.