The show is aimed at an up-market, 25- to 44-year-old male and female audience. It features the actor Charlie Sheen playing a rich bachelor who has to cope with a child for the first time when his nephew comes to stay.
The ads, which run for a month from 2 July, aim to drive viewers to the channel and to make the show an appointment to view. Two 30-second TV ads will run on national terrestrial and satellite channels while radio spots will air on local stations in the four major cities London, Manchester, Newcastle and Birmingham.
In one TV spot, a father brings the wrong child home from a shopping trip, to the horror of his wife.
Chris Hancox, the director of sales and marketing for Paramount Comedy, said: "The campaign uses British humour to introduce a brand new series to our viewers in a way that combines the essence of Two and a Half Men with Paramount's key values."
The ads were written and art directed by Nik Stewart and Johnny Parker.
Media was planned and bought by Equinox.