In April, Facebook announced that it was buying Instagram in a cash and stock deal that was worth more than $1bn (£637m).
Available on iPhone and Android devices, Instagram's millions of users add filters to their photos and then share them with other people on Instagram or other web services.
The OFT has been investigating whether its merger with Facebook would restrict people from using other apps or related websites.
For example, there has been concern that the takeover would prevent people from posting their Instagram images on sites other than Facebook, such as social media rival Twitter.
But the OFT has judged that the likelihood of this is negligible and so the deal should not be handed to the Competition Commission for a more lengthy probe.
But there have been questions raised over how Facebook will recoup its massive investment in the firm by finding ways to make money from the app.
This has the backdrop of wider concerns around Facebook following a major nosedive in its share price since the company went public in May.
Facebook share values have almost halved from their initial price, after investors started to get jittery over whether the firm can capitalise on the ever-increasing use of its service on mobile devices.
Despite raising more than $16bn in the stock float to improve its operation, the company is now making less money from each user as it struggles to unlock advertising revenues and appease nervous investors.
But if Facebook can crack a way to capitalise on the massive demand and use of Instagram mobile apps, it will have a major asset should the takeover pass the final regulatory hurdles.
> Twitter attempted to buy Instagram before Facebook deal, says report
> Instagram rumoured for web service launch