Sterilisation apparatus (1) for sterilising containers (100) comprising: a vaporisation chamber (2) that receives, through an inlet, air and an aqueous composition containing a sterilising agent and outputs a mixture formed by air, water vapour and an evaporated sterilising agent; a rotary dispenser (4) having a fixed portion (5) which internally incorporates the vaporisation chamber (2) and a rotating portion (6) bearing dispensing nozzles (7), the vaporisation chamber (2) feeding the dispensing nozzles (7) with the gaseous mixture generated.