The Commission found there was no overlap in the activities of the merging entities so it was unlikely to substantially prevent or lessen competition.
KKR agreed to acquire LGC from Bridgepoint for an undisclosed amount in December.
It said at the time that there would be a particular focus on the US and Asia.
KKR is a global investment firm which offers a range of alternative asset funds and other investment products to investors.
LGC provides reference materials, genomics solutions and analytical testing products and services.
It was acquired by Bridgepoint from LGV Capital in a transaction that valued the business at £257m in 2010.
The firm has grown through investment from Bridgepoint which has enabled the acquisition of 12 companies and revenue growth from £130m in 2010 to £222m in 2015.