"He has just been offered a well-paid job with Radio Four" sounds more recent and has the intended effect in terms of communicating the timing of the offer. It uses the right tense as the present perfect tense is used to talk about events that occurred very recently.
"He was just offered a well-paid job with Radio Four" sounds a bit awkward and doesn't effectively tell the listener about when exactly the job was offered - recently or sometime in the past.
Hope I answered your question.
