The former France midfielder, who has not had a major coaching job since leaving Besiktas with two games left in the 2007 season, will replace France coach-elect Laurent Blanc.
"It was my heart's choice. I would not have come back to (coaching) in France if it was any team but Bordeaux," Tigana, a Girondins player from 1981 to 1989, told a news conference on Tuesday.
His task, however, will be tricky as Bordeaux, who finished a disappointing sixth in Ligue 1 this season, have already lost key striker Marouane Chamakh to Arsenal.
With no European competition on the 2010/11 menu, Yoann Gourcuff could also leave after Olympique Lyon president Jean-Michel Aulas expressed his interest in the France playmaker.
"I know that it will be a tough challenge," said Tigana.
"We will try to be intelligent. Maybe we will need to have fewer players in the squad and rely on our young prospects."
The much-travelled 54-year-old, who has coached Olympique Lyon, Monaco and Fulham, was expected to sign a two-year contract, according to French media reports.
ENERGY SAPPING
A prominent member of France's great side of the 1980s alongside Michel Platini, Mali-born Tigana won 52 caps for France and helped win the European championship in 1984.
A pocket-sized and skilful midfielder, he helped Bordeaux win three French titles before moving to Olympique Marseille, where he won the league twice more before ending his playing career in 1991.
Tigana will take over a side, who, under the guidance of former France defender Blanc, finished Ligue 1 runners-up in 2008 and won the title in 2009.
They started well this season, leading halfway through, but then collapsed.
Bordeaux also reached the quarter-finals of the Champions League this season, losing to Ligue 1 rivals Olympique Lyon.
Tigana, who also was a candidate for the French job with Blanc when Domenech was appointed in 2004, left his last two jobs under something of a cloud but won a 2 million pounds High Court payout from Fulham for wrongful dismissal.
After his Besiktas experience, Tigana said he needed a break from the game.
"I had a little health problem and then I went on a humanitarian mission in Mali," he said. "And I always need a break (after a coaching job) because it is an energy-sapping job."
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