The six-strong lobbying firm will keep the same name after the two directors agreed a deal with parent firm Unique Communications Group.
MacDuff declined to reveal any figures. He said the deal comprised an upfront payment and deferred earnings for a two-year period.
He claimed the move would help Precise work more closely with other agencies, including financial PR firms.
Lowe said the agency would now provide 'focused government relations consultancy, while learning to dovetail services with other comms consultancy firms'.
Precise Public Affairs was established in January 2002, as a division of Unique Communications Group, which used to be chaired by the broadcaster Noel Edmonds.
The agency's current retained clients include Scottish & Newcastle, the EU-Russia Centre, Hilton Hotels Corporation and Cemex.
MacDuff is a former MD of Strategy in Scotland, part of Grayling Group, and before that worked as a researcher to Labour MPs.
Before joining Precise, Lowe was head of public affairs at PricewaterhouseCoopers and also held senior positions in the public affairs department at brewer Scottish & Newcastle.