Soares had been linked with a move to the Gunners for the last couple of weeks and the likelihood of a transfer accelerated when Southampton brought in Kyle Walker-Peters on loan.
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The move gives the Gunners some much-needed cover at full-back and it is expected to allow Ainsley Maitland-Niles to push into midfield.
"For me, Arsenal is a top team." Cedric told the club's website.
"They are a very, very good club, with fantastic fans as well. They are known to be so well supported and for me, it's a pleasure to be here.
"Like I said, it's a dream come true because I always thought about coming here and imagined it, and seeing it happen is really amazing."
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"Cedric is a defender with good experience of the Premier League, and of course at international level." Technical director Edu said. "He is another strong addition to our defensive unit who will provide our squad with quality. I know he is a player who plays with absolute full commitment and energy. We are all looking forward to going into the last stages of the season with Cedric as part of the club.”
In their statement Southampton described the loan fee they received for Cedric as "significant."
Walker-Peters joined Southampton on Wednesday, with the Tottenham full-back moving on loan for the rest of the season. Asked if signing Walker-Peters would allow Soares to move away, Saints boss Ralph Hasenhuttl said: "From our side yes.”
Hasenhuttl added: "The fact is that he's out of contract in the summer. He is injured at the moment so it will take three or four weeks until he can play again.
"We had a good meeting two days ago. We didn't speak about that. I was very positive with his development of his game in our shape, I could also imagine going longer with him but sometimes things change quickly in football.
"For the club and for him it's best and we say 'Okay, if you want to leave, you only have two or three months on your contract and it's better to go and we are concentrating on developing other players."
Walker-Peters made just 24 senior appearances for Spurs, including five this season, while Soares has been a Southampton regular since joining in 2015.
However, with 28-year-old Soares’ contract expiring in the summer, Hasenhuttl explained it is Southampton’s philosophy to turn to youth.
"This is our way, this is our philosophy,” he said. “We went this way for more than a year and see young players developing well. We have a few bright diamonds in our youth and we will have a lot of fun with them in the future and Kyle Walker-Peters can be one of them."