We present an end-to-end voice-based conversational agent that is able to engage in naturalistic multi-turn dialogue and align with the interlocutor's conversational style. The system uses a series of deep neural network components for speech recognition, dialogue generation, prosodic analysis and speech synthesis to generate language and prosodic expression with qualities that match those of the user. We conducted a user study (N=30) in which participants talked with the agent for 15 to 20 minutes, resulting in over 8 hours of natural interaction data. Users with high consideration conversational styles reported the agent to be more trustworthy when it matched their conversational style. Whereas, users with high involvement conversational styles were indifferent. Finally, we provide design guidelines for multi-turn dialogue interactions using conversational style adaptation.