The 27-year-old joined the French Top 14 club in 2015 and was a member of the side which beat Quins in the European Challenge Cup final in May.
South Africa-born Catrakilis has previously played for Super Rugby franchises Southern Kings and Stormers in his homeland.
He also won the Currie Cup twice with Western Province.
"The fly-half position is hugely influential in the game and Demetri has all the physical and mental attributes required to dominate at the highest level," Harlequins director of rugby John Kingston said.
"Our ability to secure this signing already is a reflection of our commitment to focus hugely on Harlequins' recruitment needs for the future."
Quins have not disclosed the length of Catrakilis' contract at The Stoop.

The National Lottery windfall has been won with a ticket bought somewhere in Denbighshire for the 1 April draw.
It matched the Lotto Millionaire Raffle draw - AQUA 6323 7030 - but no-one has come forward.
The mystery ticket holder has until the end of September to submit their claim - otherwise the money will go to lottery good causes.
"We're urging everyone who bought a Lotto ticket in this area to check their old tickets again or look anywhere a missing ticket could be hiding," said Andy Carter from the National Lottery.
"Try checking in the pockets of clothing, in wallets, bags and down the back of the sofa - someone out there could literally be sitting on a fortune."

Vonn finished 0.70 seconds clear of Switzerland's Lara Gut, with Austrian Cornelia Huetter a further 0.55 seconds back in Altenmarkt Zauchensee.
The American also won Saturday's downhill event.
That equalled Annemarie Moser-Proll's record tally of 36 World Cup downhill wins.
The 31-year-old now has 73 overall World Cup wins - 13 short of Ingemar Stenmark's record.
Vonn leads the World Cup super-G standings by 80 points over Hutter, and is now within 38 points of Lara Gut in the overall standings.
"It's a perfect start to the new year," she said. "Hopefully I can just continue on in this direction and keep winning."
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Harlequins have agreed a deal to sign Montpellier fly-half Demetri Catrakilis ahead of the 2017-18 season.
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The search is on for the winner of an unclaimed winning lottery ticket worth £1m.
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Lindsey Vonn claimed her second win in two days at the Alpine Skiing World Cup event in Austria with victory in the super-G event.