Software engineering researchers have, over the years, proposed different critical success factors (CSFs) which are believed to be critically correlated with the success of software projects. To conduct an empirical investigation into the correlation of CSFs with success of software projects, we adapt and extend in this work an existing contingency fit model of CSFs. To archive the above objective, we designed an online survey and gathered CSF-related data for 101 software projects in the Turkish software industry. Among our findings is that the top three CSFs having the most significant associations with project success were: (1) team experience with the software development methodologies, (2) team's expertise with the task, and (3) project monitoring and controlling. A comprehensive correlation analysis between the CSFs and project success indicates positive associations between the majority of the factors and variables, however, in most of the cases at non-significant levels. By adding to the body of evidence in this field, the results of the study will be useful for a wide audience. Software managers can use the results to prioritize the improvement opportunities in their organizations w.r.t. the discussed CSFs. Software engineers might use the results to improve their skills in different dimensions, and researchers might use the results to prioritize and conduct follow-up in-depth studies on those factors.