We present radio and infrared (3.6-24um) counterparts to submillimetre galaxies (SMGs) detected in the Extended Chandra Deep Field South with the LABOCA 870-um bolometer camera on the 12-m Atacama Pathfinder Experiment. Using the Very Large Array at 1.4GHz and Spitzer we have identified secure counterparts to 79 of the 126 SMGs (SNR>3.7, S_870>4.4mJy) in the field, 62 via their radio and/or 24-um emission, the remainder using a colour-flux cut on IRAC 3.6- and 5.8-um sources chosen to maximise the number of secure, coincident radio and 24-um counterparts. In constructing our radio catalogue, we have corrected for the effects of `flux boosting, then used the corrected flux densities to estimate the redshifts of the SMGs based on the radio/submm spectral indices. The effect of the boosting correction is to increase the median redshift by 0.2 resulting in a value of z=2.2 (+0.7-0.8) (1-sigma errors) for the secure radio counterparts, in agreement with other studies, both spectroscopic and photometric.