The OFT said the takeover raised "no competition concerns in any market". In replica kit sales, it argued that although the pair have a high combined market share of over 45%, this "overstates the rivalry between them".
Its statement continued: "Club kits and England kits are not significant competitive alternatives, and Umbro's leading position is principally based on its England kit deal, while Nike's sales derive from its club kit deals."
The OFT also ruled out concerns that allowing Umbro to come under Nike's control would make price-fixing or other collusion between the companies' rivals more likely post-merger.
Sports clothes and equipment retailer JJB Sports holds a 10% stake in Umbro, which it built up when Umbro first received the approach from Nike.
Umbro has supplied the England football team's kit for more than 20 years.