This paper shows that the automatic labeling of discourse connectives with the relations they signal, prior to machine translation (MT), can be used by phrase-based statistical MT systems to improve their translations. This improvement is demonstrated here when translating from English to four target languages - French, German, Italian and Arabic - using several test sets from recent MT evaluation campaigns. Using automatically labeled data for training, tuning and testing MT systems is beneficial on condition that labels are sufficiently accurate, typically above 70%. To reach such an accuracy, a large array of features for discourse connective labeling (morpho-syntactic, semantic and discursive) are extracted using state-of-the-art tools and exploited in factored MT models. The translation of connectives is improved significantly, between 0.7% and 10% as measured with the dedicated ACT metric. The improvements depend mainly on the level of ambiguity of the connectives in the test sets.