Vaccine hesitancy was one of the ten major threats to global health in 2019, according to the World Health Organisation. Nowadays, social media has an important role in the spread of information, misinformation, and disinformation about vaccines. Monitoring vaccine-related conversations on social media could help us to identify the factors that contribute to vaccine confidence in each historical period and geographical area. We used a hybrid approach to perform an opinion-mining analysis on 1,499,227 vaccine-related tweets published on Twitter from 1st June 2011 to 30th April 2019. Our algorithm classified 69.36% of the tweets as neutral, 21.78% as positive, and 8.86% as negative. The percentage of neutral tweets showed a decreasing tendency, while the proportion of positive and negative tweets increased over time. Peaks in positive tweets were observed every April. The proportion of positive tweets was significantly higher in the middle of the week and decreased during weekends. Negative tweets followed the opposite pattern. Among users with ≥2 tweets, 91.83% had a homogeneous polarised discourse. Positive tweets were more prevalent in Switzerland (71.43%). Negative tweets were most common in the Netherlands (15.53%), Canada (11.32%), Japan (10.74%), and the United States (10.49%). Opinion mining is potentially useful to monitor online vaccine-related concerns and adapt vaccine promotion strategies accordingly.