Time‐variable transit time distributions (TTDs) have been utilized as a tool to understand how catchments transmit water. However, most of the existing TTD estimation methods require to impose certain structures on those TTDs a priori, which could lead to misinterpreting data. We present a data‐based method to estimate time‐variable TTDs without imposing their structure a priori. The core of the method is the use of a revised flow‐weighted time, where TTDs do not reflect variable external forcings directly. The functional forms of the TTDs are much simpler in flow‐weighted time, compared to those in calendar time, and this allows for easier estimation of TTDs. Dynamic (state‐dependent) multiple linear regression methods were applied to estimate the time‐variable TTDs in flow‐weighted time, which can eventually be transformed back to calendar time. The method performs well in a proof‐of‐concept demonstration with synthetic data sets. We also discuss potential generalizations of the proposed method. Key Points We outline a data‐based method to estimate transit time distributions (TTDs) without imposing their structure a priori We use a (dynamic) multiple linear regression method to estimate (time‐variable) TTDs in flow‐weighted time In a proof‐of‐concept demonstration, the method estimates TTDs close to the actual TTDs