Tool condition monitoring is increasingly important as a widespread application of automated, computer numerically controlled machining in a variety of modern industries. Although a significant amount of research on tool condition monitoring in machining has been conducted during the past few decades, the research is primarily focused on tool flank wear. Less attention is paid to tool-edge wear, which is a critical issue in high-speed finish machining where the feed rate is in the same magnitude as tool edge dimensions, and thus, the tool cutting edge is subjected to extensive mechanical and thermal deformation. The present study fills this important research gap in tool condition monitoring. This paper presents a method of monitoring tool-edge wear in the high-speed finish machining of an aerospace superalloy Inconel 718 by extracting Hoelder exponents from wavelet transform analysis of cutting vibrations. A total of 60 cutting experiments were conducted, covering a range of cutting speed and feed rate conditions. The experimental results show that cutting vibrations increase as tool-edge wear develops. Wavelet transform analysis can be employed to identify single local maxima of the cutting vibration signals. As tool-edge wear develops, the values of Hoelder exponents vary from 0.55 to 0.90. It is suggested that under the cutting conditions tested in the present study, 0.8 can be used as the threshold value of Hoelder exponents to differentiate severe and normal tool-edge wear.