It said the deal raised no competition concerns, despite both companies being active in the fleet market.
Details of the deal, worth more than £1 billion, were announced earlier this year. The move is part of a bid by Volkswagen to become a global mobility group.
LeasePlan was sold by ABN AMRO Bank, which stated several years ago that it intended to dispose of its global leasing division.
Two years ago Volkswagen was one of the leading companies in the bid to buy the leasing giant, which operates more than 120,000 vehicles in the UK.
Announcing the deal earlier this year, Dr Bernd Pischetsrieder, chief executive officer of Volkswagen Group, says: “This acquisition is a milestone for us and consistently follows our strategic roadmap to a global mobility group. Together with our partners, we have acquired an extremely successful and profitable company.”
The consortium includes two Middle Eastern financial investment companies.