"My role will transition to being exec chair & CTO, overseeing product, software & sysops," Musk said in a tweet, adding that she would start in the job in about six weeks.
Musk said in November he expected to reduce his time at Twitter and eventually find a new leader to run the social media company.
The move is likely to allay Tesla investors' concerns, who have been increasingly worried about the time that Musk is devoting to turning around Twitter.
Tesla Inc TSLA.O shares jumped 2.4% in volume spike on the news.
Twitter users in December voted to oust owner Musk as chief executive in an unscientific poll he organized and promised to honor, just weeks after he took charge of the social media giant.
The billionaire's first two weeks as the new Twitter owner in October were marked by rapid change. He quickly fired Twitter's previous CEO Parag Agrawal and other senior leaders and then laid off half its staff in November.
Some information in this report came from Agence France-Presse.
