Gourcuff signed a five-year contract after passing a medical, Lyon chairman Jean-Michel Aulas told a news conference.
The 24-year-old, who moves for a fee of 22 million euros, could play his first Ligue 1 match for Lyon on Saturday at Lorient, a club coached by his father, Christian Gourcuff.
"I hope to keep improving, to work well and blend in with the team and the coach's plans," Gourcuff said in Lyon. "We have a quality squad. I hope we will achieve great things and win titles."
The elegant Gourcuff, widely regarded as France's most gifted player, joined Bordeaux in 2008 from AC Milan and helped them win the Ligue 1 title in 2009.
He was voted Ligue 1 Player of the Year in 2009 but was blamed for Bordeaux's poor run of form at the end of last season which saw them finish sixth and miss out on a place in Europe.
Gourcuff also suffered from France's shameful World Cup performance and has been a shadow of his brilliant best since the start of the current campaign.
His transfer is the most spectacular deal in Ligue 1 during a transfer period that has been quiet so far and closes on Aug. 31.
"Yoann has exactly the profile we were looking for," Lyon coach Claude Puel told Wednesday's news conference. "I hope he can help us reach another level."
