Sentiment Analysis on Twitter Data is indeed a challenging problem due to the nature, diversity and volume of the data. People tend to express their feelings freely, which makes Twitter an ideal source for accumulating a vast amount of opinions towards a wide spectrum of topics. This amount of information offers huge potential and can be harnessed to receive the sentiment tendency towards these topics. However, since no one can invest an infinite amount of time to read through these tweets, an automated decision making approach is necessary. Nevertheless, most existing solutions are limited in centralized environments only. Thus, they can only process at most a few thousand tweets. Such a sample is not representative in order to define the sentiment polarity towards a topic due to the massive number of tweets published daily. In this work, we develop two systems: the first in the MapReduce and the second in the Apache Spark framework for programming with Big Data. The algorithm exploits all hashtags and emoticons inside a tweet, as sentiment labels, and proceeds to a classification method of diverse sentiment types in a parallel and distributed manner. Moreover, the sentiment analysis tool is based on Machine Learning methodologies alongside Natural Language Processing techniques and utilizes Apache Spark's Machine learning library, MLlib. In order to address the nature of Big Data, we introduce some pre-processing steps for achieving better results in Sentiment Analysis as well as Bloom filters to compact the storage size of intermediate data and boost the performance of our algorithm. Finally, the proposed system was trained and validated with real data crawled by Twitter, and, through an extensive experimental evaluation, we prove that our solution is efficient, robust and scalable while confirming the quality of our sentiment identification.