The invention relates to a closing assembly for containers, such as bottles and/or jars, which allows a hermetically isolated additive to be dispensed into the inside of said container, via a cartridge, characterised in that the assembly comprises a closing device having a main body (3) with joining means that allow detachable connection to a removable cartridge (4) storing the additive to be released, where said removable cartridge (4) houses a piercing projection (5) that can be actuated by direct contact with an actuator (2) connected to said main body (3).