Recent work has proposed artificial intelligence (AI) models that can learn to decide whether to make a prediction for an instance of a task or to delegate it to a human by considering both parties' capabilities. In simulations with synthetically generated or context-independent human predictions, delegation can help improve the performance of human-AI teams -- compared to humans or the AI model completing the task alone. However, so far, it remains unclear how humans perform and how they perceive the task when they are aware that an AI model delegated task instances to them. In an experimental study with 196 participants, we show that task performance and task satisfaction improve through AI delegation, regardless of whether humans are aware of the delegation. Additionally, we identify humans' increased levels of self-efficacy as the underlying mechanism for these improvements in performance and satisfaction. Our findings provide initial evidence that allowing AI models to take over more management responsibilities can be an effective form of human-AI collaboration in workplaces.