"After much thought I have decided to dedicate my future to my family," Norman, 41, said in a statement on Wednesday. "With two young kids at home, now is the right time for me to be with them.
"I could not have had a better player to work with and this has been one of the most difficult decisions I have ever had to make."
Wawrinka did not defend his U.S. Open title this year after a knee injury ended his season in August.
"I would like to thank Magnus for the amazing four years we had together," he said. "I will always be grateful for the work and the time he spent on me to make me improve and become a three-time grand slam champion.
"He was not only part of my team but also part of the family. For now, I'm focusing on my rehabilitation and I will take time to decide with my team the necessary next steps."
The Swiss was ranked third in the world in July, but has slipped to ninth following his injury layoff.
(Writing by Simon Jennings in Bengaluru, editing by Ed Osmond)
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