(1) Background: So far, research results have confirmed the relationship between heat and cold stress, the fluctuations in atmospheric pressure and high relative humidity, and the vulnerability of patients with so-called “weather-dependent” diseases which could lead to death. This study aimed to determine the meteorological parameters, their interactions, and the seasonal changes of the most significant factors in predicting the number of patients reporting to the Emergency Departments (EDs) in Poznań (Poland) during 2019. (2) Methods: The analysis included the meteorological parameters and data of 3606 patients diagnosed with essential or complicated arterial hypertension, myocardial infarction, chronic ischemic heart disease, and ischemic or unspecified stroke by the International Classification of Diseases (ICD-10). The meteorological data (days per week and seasonal data) were used to build a linear regression model to assess the changes in the daily number of reporting patients. The input data for the final model were selected based on the principal component analysis (PCA), and built for each delay and acceleration (reporting up to 3 days before the change or up to 3 days after the change of the meteorological parameter). (3) Results: A significantly lower number of reports was observed during weekends compared to working days (standardised b = −0.254, p-value < 0.0001) and three days before the maximum daily air temperature in the spring and summer period (standardised b = −0.748, p-value < 0.0001), while two days after the increase in the daily amplitude of atmospheric pressure (standardised b = 0.116, p-value = 0.0267), and also on the day of occurrence of the unfavourable interdiurnal air temperature change, an increase in the number of patients was noted (standardised b = 0.115, p-value = 0.0186). The changes in the last two parameters were statistically insignificant. Based on the obtained results, the negative impact of the changes in the meteorological conditions on the number of reports to the EDs in Poznań was determined.