Eighteen-year-old defender Saliba will spend next season on loan at the Ligue 1 club before linking up with the Gunners next year.
Saliba was the second deal confirmed in the space of two hours by the Premier League club after the capture of Ceballos on a season-long loan.
Arsenal are believed to have been interested in the teenager for some time and but finally landed their man.
"Highly rated French defender William Saliba is joining us from Ligue 1 club Saint-Etienne on a long-term contract," the club announced on their official website.
"The much sought-after centre-half will spend a season back on loan at St Etienne before joining our squad next summer."
"It's a massive pleasure to sign for a really, really big English club," Saliba told Arsenal's official website.
"This is the biggest club in England for me, so it was an easy decision. I didn't think twice about signing here, so I'm really happy."
Head coach Unai Emery added: "We're delighted William is joining us. Many teams wanted him but he decided he wanted to come to us and be part of our future."
Arsenal had earlier announced the season-long loan signing of midfielder Ceballos.
The 22-year-old Spain international, who made 23 La Liga appearances in the 2018/19 campaign, helped Spain's Under-21s to European glory last month.
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