U.S. online retailer Amazon.Com is to buy the 58 percent of British DVD and games rental firm Lovefilm it does not already own for an undisclosed price, it said on Thursday.

Lovefilm, whose Europe-focused business has a similar model to U.S. video rental firm Netflix Inc, has built a movie rental-by-post business and has also started streaming digital movies.

Lovefilm and Amazon have enjoyed a strong working relationship since Lovefilm acquired Amazon Europe's DVD rental business in 2008, Greg Greeley, Amazon's Vice President of European Retail, said.

It's a natural complement to our business because we already have the retail offer.

Amazon owned a 42 percent stake in privately held Lovefilm after combining its own European rental operation with Lovefilm in 2008 and through buying out one of the company's venture capital backers.

Lovefilm's chief executive Simon Calver, who is staying with the firm, said Amazon's retail expertise would help accelerate growth for the company, which has nearly 1.6 million members in the UK, Germany, Sweden, Denmark and Norway.

With Amazon's unequivocal support we can significantly enhance our members' experience across Europe, he said.

Lovefilm investors Balderton Capital, DFJ Esprit and Index Ventures welcomed the deal.

Under the great management team of Simon Calver, Lovefilm has built a substantial business with over $100m in revenues and significant operating profits, Index Ventures partner Saul Klein said in his blog.

To do this anywhere is great, to do this in the UK and Europe, makes Lovefilm a real success story.

Lovefilm, which launched in 2004, has started streaming new films to members, most recently on Internet-connected Sony Playstation 3 games consoles.

It's early days but we've made huge inroads into the digital space, Calver said.

We are delighted with what we are seeing on the digital side, and with under 5 percent of UK households having Lovefilm membership, we still see a huge amount of runway for the physical product as well.

(Editing by Dan Lalor and Jon Loades-Carter)

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