Gourcuff will sign a long-term contract after passing a medical, Lyon said in a statement.
The statement said the clubs had agreed on a transfer fee of 22 million euros, plus 4.5 million for Bordeaux if Lyon were to sell him later to another club.
"Lyon welcome the arrival of Yoann Gourcuff, who was the main target of coach Claude Puel and will give the team a new dimension in midfield," it said.
Gourcuff, 24, who has won 22 caps for France, was expected to leave Bordeaux since new Girondins coach Jean Tigana left him out of the starting lineup for his side's 2-1 win at Paris St Germain in Ligue 1 on Sunday.
The elegant Gourcuff, widely regarded as France's most gifted player, joined Bordeaux in 2008 from AC Milan and helped Girondins win the Ligue 1 title in 2009.
He was voted Ligue 1 Player of the Year in 2009 but was later blamed from Bordeaux's poor run of form at the end of last season when the finished sixth and missed out on a place in Europe.
Gourcuff also suffered from France's shameful World Cup performance and has only been the shadow of his brilliant best since the start of the current campaign.
If finalised, his transfer would become the most spectacular deal in Ligue 1 during the transfer window which closes on August 31 and had been fairly quiet in France so far.
