There is an asymmetry between the origin (Source; move from X…) and end-point (Goal; …to Y) of motion events in both language and memory: Goals are mentioned more often and remembered more accurately than Sources. Here, we pursue the hypothesis that this Goal bias emerges as an online attentional bias that occurs during event apprehension and itself connects to event memory and linguistic measures. We record participants' eye movements as they view or prepare to describe motion events and later test their memory of Goals or Sources. We find an online attentional bias for Goals over Sources during initial encoding of events. This bias is stronger during free inspection compared to speech planning. Moreover, the extent of the attentional Goal bias is systematically related to both language production and memory: When the bias is the greatest, the Source is not later mentioned during production and/or not remembered later at test. In sum, we provide the first evidence that the Goal bias appears during visual encoding of motion events and identify a direct relation between event apprehension and later event description and memory.