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COVID-19 pandemic has caused a global health crisis, resulting in endless efforts to reduce infections, fatalities, and therapies to mitigate its after-effects. Currently, large and fast-paced vaccination campaigns are in the process to reduce COVID-19 infection and fatality risks. Despite recommendations from governments and medical experts, people show conceptions and perceptions regarding vaccination risks and share their views on social media platforms. Such opinions can be analyzed to determine social trends and devise policies to increase vaccination acceptance. In this regard, this study proposes a methodology for analyzing the global perceptions and perspectives towards COVID-19 vaccination using a worldwide Twitter dataset. The study relies on two techniques to analyze the sentiments: natural language processing and machine learning. To evaluate the performance of the different lexicon-based methods, different machine and deep learning models are studied. In addition, for sentiment classification, the proposed ensemble model named long short-term memory-gated recurrent neural network (LSTM-GRNN) is a combination of LSTM, gated recurrent unit, and recurrent neural networks. Results suggest that the TextBlob shows better results as compared to VADER and AFINN. The proposed LSTM-GRNN shows superior performance with a 95% accuracy and outperforms both machine and deep learning models. Performance analysis with state-of-the-art models proves the significance of the LSTM-GRNN for sentiment analysis.