The performance of carbon nanotube network (CNN) devices is usually limited by the high resistance of individual nanotube junctions (NJs). We present a novel method to reduce this resistance through a nanoscale chemical vapor deposition (CVD) process. By passing current through the devices in the presence of a gaseous CVD precursor, localized nanoscale Joule heating induced at the NJs stimulates the selective and self-limiting deposition of metallic nanosolder. The effectiveness of this nanosoldering process depends on the work function of the deposited metal (here Pd or HfB2), and it can improve the on/off current ratio of a CNN device by nearly an order of magnitude. This nanosoldering technique could also be applied to other device types where nanoscale resistance components limit overall device performance.