Fake news detection is a challenging problem in online social media, with considerable social and political impacts. Several methods have already been proposed for the automatic detection of fake news, which are often based on the statistical features of the content or context of news. In this paper, we propose a novel fake news detection method based on Natural Language Inference (NLI) approach. Instead of using only statistical features of the content or context of the news, the proposed method exploits a human-like approach, which is based on inferring veracity using a set of reliable news. In this method, the related and similar news published in reputable news sources are used as auxiliary knowledge to infer the veracity of a given news item. We also collect and publish the first inference-based fake news detection dataset, called FNID, in two formats: the two-class version (FNID-FakeNewsNet) and the six-class version (FNID-LIAR). We use the NLI approach to boost several classical and deep machine learning models including Decision Tree, Naïve Bayes, Random Forest, Logistic Regression, k-Nearest Neighbors, Support Vector Machine, BiGRU, and BiLSTM along with different word embedding methods including Word2vec, GloVe, fastText, and BERT. The experiments show that the proposed method achieves 85.58% and 41.31% accuracies in the FNID-FakeNewsNet and FNID-LIAR datasets, respectively, which are 10.44% and 13.19% respective absolute improvements.