Both agencies are set to pick up the business following an official tender that kicked off in September last year.
The media accounts for both the Post Office and the Royal Mail will transfer from incumbent OMD. MediaCom Edinburgh was also involved in the pitch for the Royal Mail business.
The pitch process was concluded by an e-auction, which took place last Friday (27 January).
There is now a legal "cooling-off period" of 10 days in place before the announcement can be made officially, according to sources.
Mindshare and UM London will now be tasked with improving the return on investment across print, TV radio and digital media.
OMD has held the media planning and buying account for the Post Office since 2006.
The media review follows on the heels of a pitch for the Post Office's advertising account that led to Dare being appointed to the business in January. The previous incumbent on the creative account had been Mother.
Abbott Mead Vickers BBDO is the current incumbent on the Royal Mail's advertising account, while Proximity London oversees the brand's digital and direct marketing activity.
Both Mindshare and Universal McCann referred calls to the Royal Mail Group.
A spokesman for the Royal Mail Group, said: "We are not in a position to announce the result of these media pitches until the process has been completed."
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