We present a reliable and robust integrated fluorescence detector capable of detecting single atoms. The detector consists of a tapered lensed single-mode fiber for precise delivery of excitation light and a multimode fiber to collect the fluorescence. Both are mounted in lithographically defined SU-8 holding structures on an atom chip. 87Rb atoms propagating freely in a magnetic guide are detected with an efficiency of up to 66%, and a signal-to-noise ratio in excess of 100 is obtained for short integration times.