The US Federal Trade Commission has given the go-ahead for Facebook's takeover of popular photo-sharing app Instagram.

In a short statement, the US regulator said that it had "closed its non-public investigation of Facebook's proposed acquisition of Instagram without taking any action", meaning the deal can now "proceed as proposed".

Instagram appeared to have got a great deal when Facebook shares started trading in mid-May at $38, but that turned sour after Facebook saw a dramatic slide in its stock price to around $20, meaning the deal is now valued at around $735m.

This means that the company's founders Kevin Systrom and Mike Krieger are out of pocket to the tune of around $300m - on paper at least. The share price could also, of course, go up again making their stock more valuable.

Since it launched in 2010, Instagram on iPhone and Android devices has secured more than 50 million users, who apply filters to their photos and then share them with other users.

Facebook said in a statement that it was pleased to secure FTC approval for the Instagram deal, and indicated that it hopes to complete the transaction by the end of 2012.