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The 28-year-old will be out of contract in June, having made more than 100 appearances for the Saints since joining them from Sporting Lisbon in 2015.
Right-back Soares, who had a loan spell at Inter Milan last season, is currently recovering from a knee problem, so his debut for the Gunners could be delayed until after the winter break.
Arsenal technical director Edu said on the club website: "Cedric is a defender with good experience of the Premier League, and of course at international level.
"He is another strong addition to our defensive unit who will provide our squad with quality."
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Southampton had brought in Kyle Walker-Peters on loan from Tottenham as cover.
"The club would like to thank Cedric for all his efforts during his time with the club and wish him luck for the rest of the campaign," a Southampton statement read.
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