The 24-year-old has the difficult task of trying to replace Belgium's Eden Hazard who joined Chelsea earlier this month. Hazard has been named best Ligue 1 player in the last two years.
Lille did not give any financial details but French media said the transfer fee for Martin was about 10 million euros (£8.1m).
"I wanted to sign for Lille as they're an ambitious club who I've been interested in for ages. Whether it's Yohan Cabaye, Adil Rami or Mathieu Debuchy, they've all advised me to join Lille," he said referring to his France team mates.
"During my short career I've not had the chance to win many trophies. I hope to win some here," he told the Lille website.
Known for his passing skills, Martin has set up 25 goals and scored five in the past two seasons at Sochaux, who he helped to a surprise fifth-place finish in Ligue 1 in 2011.
Martin, who has 14 caps, is at Euro 2012 where he has made two substitute appearances for France in the group stage.
He made a stunning debut last year by scoring twice in a 4-1 win over European Championship co-hosts Ukraine in a friendly.
Lille, the 2011 French champions, finished third last season and will play in next season's Champions League playoff round.