Uncertainties and changes in software requirements have compelled companies to become more agile in software development projects. To keep pace with the agile environment, companies incorporate agile software development methodologies into their projects. However, the way that the agile methodology is implemented may determine the success of the project. This study aims to understand critical success factors affecting agile projects' success from the perspectives of agile practitioners. First, an extensive systematic literature review was conducted with the detailed examination of the Agile Manifesto, Agile Principles, and Scrum Guide to develop the Agile Software Project Success Model. Second, refinement of the factors was conducted through one-on-one meetings with six agile practitioners, and then a group meeting was conducted to reach a consensus on the model. Finally, using IBM Amos 20.0, data collected from 596 agile practitioners were used to understand the relationships defined in the research model. Results indicated that all the hypotheses except two of them were supported. Among the factors, customer factors and agile process factors are the stronger predictors of process efficiency, sustainable software product quality and stakeholder satisfaction compared to other factors. This study concludes with the theoretical and practical implications and recommendations for possible future studies.