Murray has been without a coach since parting ways with Ivan Lendl in March.
Mauresmo coached Marion Bartoli to the Wimbledon title last year, and has previously acted in a similar capacity for Michael Llodra.
She began coaching after retiring from a playing career in which she won Wimbledon and the Australian Open.
She has also been the captain of France's Fed Cup team since 2013.
Murray said in a statement: "I’m excited by the possibilities of the new partnership and Amelie is someone I have always looked up to and admired. She’s faced adversity plenty of times in her career, but was an amazing player and won major titles, including Wimbledon.
"I have a very strong coaching team already in place, but I think Amelie brings with her experience and tactical expertise and will push us all to improve. Everyone I know talks very highly of Amelie, as a person and coach, and I’m convinced that her joining the team will help us push on – I want to win more Grand Slams."
The appointment has not come as a surprise to several tennis big names, such as Billie Jean King, who tweeted Murray earlier this week:
And Mats Wilander suggested last month that Mauresmo would be an ideal advisor for the British number one.
Mauresmo said: "I’m really excited to be able to work with Andy. He’s an amazingly talented tennis player and I feel I have plenty to offer both him and the team around him. I’m looking forward to getting down to work and helping him win more Grand Slams.”
She later added on Eurosport: "I was surprised to be honest. I guess it's a big story to write (a woman coaching a man) but it's not my concern right now. I'm happy with the challenge; I want to help him.
"He wants to win Grand Slams, that's the goal. He has the most pressure (more than Mauresmo). I know what it is. It will change my life and my retirement, but I'm passionate about this sport, I like challenges.
"I like to put myself on the line and we'll see what I can do."
- Sports & Recreation
- Ivan Lendl