Cognitive control, the ability of a system to adapt to the demands of a task, is an integral part of cognition. A widely accepted fact about cognitive control is that it is context-sensitive: Adults and children alike infer information about a task's demands from contextual cues and use these inferences to learn from ambiguous cues. However, the precise way in which people use contextual cues to guide adaptation to a new task remains poorly understood. This work connects the context-sensitive nature of cognitive control to a method for meta-learning with context-conditioned adaptation. We begin by identifying an essential difference between human learning and current approaches to meta-learning: In contrast to humans, existing meta-learning algorithms do not make use of task-specific contextual cues but instead rely exclusively on online feedback in the form of task-specific labels or rewards. To remedy this, we introduce a framework for using contextual information about a task to guide the initialization of task-specific models before adaptation to online feedback. We show how context-conditioned meta-learning can capture human behavior in a cognitive task and how it can be scaled to improve the speed of learning in various settings, including few-shot classification and low-sample reinforcement learning. Our work demonstrates that guiding meta-learning with task information can capture complex, human-like behavior, thereby deepening our understanding of cognitive control.