The transactions are to be carried out as share deals in which Geo offers 3.45 new shares of Geo for each share of DOFCON.
Geo also said that it will also "as soon as practically possible" make an offer for all remaining shares.
DOF is the majority shareholder of Geo with a 51.1% stake.
DOFCON operates seven multi-purpose support vessels.
Geo, based in Astveit in Norway, provides offshore survey, maintenance, construction support and subsea engineering services, and owns a fleet of 16 vessels. The company is listed on the Oslo Stock Exchange and traded under the ticker GEO.
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