A statement from the French Tennis Federation on Thursday confirmed the U-turn by the 39-year-old who had been named in June to become the first woman to captain the Davis Cup team.
Mauresmo was to due take over from Yannick Noah, whose third stint in charge ended in a disappointing defeat by Croatia in last month's final held in Lille's soccer stadium.
"(Amelie Mauresmo) has accepted this challenge and renounces the position of captain of the Davis Cup France team to carry out this mission," the statement said.
"The French Tennis Federation supports and encourages this project which serves the interests of French tennis."
Pierre Cherret, the FFT's National Technical Director, said he would begin the process of finding a new Davis Cup captain who would also be responsible for the men's team at the 2020 Olympic Games in Tokyo.
"It was important and logical for Lucas, after his fruitful collaboration with Emmanuel Planque, to look for the person most likely to continue his development," Cherret said.
Mauresmo, a two-time Grand Slam champion who has also coached Britain's former world number one Andy Murray, will begin working with Pouille in preparation for the new season.
The 24-year-old world number 32 is looking forward to starting with Mauresmo and thanked the French federation for enabling him to work with her.
"I'm sure we're going to do great things together." (Reporting by Martyn Herman in London; editing by Ken Ferris)
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