The agency triumphed following a three-way pitch against undisclosed agencies, and will now work on a campaign scheduled to launch in mid-September.
The work will support the above-the-line campaign devised by Beattie McGuinness Bungay, promoting the company's long-haul destinations and the amount of legroom it offers in economy class.
First Choice has used various digital agencies for its online advertising in the past, but in the past six months has focused on pay-per-click activity to drive holiday bookings.
The company is currently reviewing its £5 million media planning and buying account in an attempt to consolidate its online and offline media activity into one agency.
Rebecca Edwards, First Choice's advertising communications manager, said the company wanted to interact with consumers online "either to disrupt their time on the net or when they're in the mindset of choosing a holiday".
Sam Ball, LMFM's creative partner, said: "First Choice is up for doing interesting advertising and so are we. We can't wait to get stuck in."