Paradigm already has a flow solutions business in Kintore, Aberdeenshire and a drilling arm in nearby Inverurie.
The deal for GeoKey, based in Edzell, Angus, is likely to see staff numbers rise from 11 to 25 by the end of next year.
The company,founded in 2007, is said to be a specialist in tubing conveyed perforating (TCP) techniques, which help well operators to improve flow rates.
Fraser Innes, Paradigm chief executive, said: "GeoKey is a big success story with a strong track record for growth and service excellence, and the company is a great strategic fit for the Paradigm Group's eagerly anticipated new well intervention technology.
"As the new technologies we have been incubating across the group start to arrive, we expect a significant ramp up in both the revenue and earnings forecast for 2014. Indeed, our current expectations are that revenues will increase to over £30 million.
"We have had extremely strong trading in 2013 across all the group companies, securing new contracts and growth globally. The acquisition of Geokey will give us a platform for our next generation well intervention services as well as continuing its current planned growth in the core TCP business."