Officers and soldiers from the group told CNN they will pull back to a position 12 miles north of Goma, but will leave a 100-strong contingent at the city's airport in line with a plan drawn up by African leaders.
Goma, a city of a million people, remained calm Wednesday morning and residents were going about their normal activities.
Rebels seized the key city in eastern DR Congo last week after days of fighting government forces.
More than 140,000 people have been displaced by the latest violence.
African leaders who convened in Uganda during the weekend demanded that M23 forces withdraw from Goma, stop all war activities and stop talking about overthrowing the government.
In return, they called on the Congolese government to listen to the rebels' grievances and attempt to resolve them.