We demonstrate for the first time a technology which allows the monolithic integration of both p-Type (InAs-Si) and n-Type (InAs-GaSb) heterojunction Tunnel FETs (TFET) laterally on a Si substrate. The lateral heterojunction nanowire (NW) structures are implemented using top-down CMOS-compatible processes combined with Template-Assisted Selective Epitaxy (TASE)  of the III-V materials. Sub-40nm InAs-Si p-TFETs and InAs-GaSb n-TFETs have been fabricated and represent to the best of our knowledge the first lateral III-V heterostructure NW TFETs. The InAs-Si p-TFETs show excellent performance with average subthreshold swing, SSave, of ∼70mV/dec. combined with an on-current, Ion, of 4μA/μm at VDS = VGS =-0.5V. The InAs-GaSb n-TFETs have about an order of magnitude higher Ion, but SS is deteriorated due to high interface traps density (Dit).