The firefighting response to the incident would scale back from 17:00 BST, the service said.
Fire crews were brought in from across the country during the height of the blaze, under the national resilience, external programme.
Lacey, who expressed his “enormous gratitude” for the additional support, said: “I want to be absolutely clear that this incident is not over.
“The nature of this landscape means fire can remain hidden underground for some considerable time, which is why we continue to ask people to stay away from the heath itself and allow our crews to work safely.”
He added that recovery work could now start with firefighters remaining at Dunwich “for as long as they are needed.”
All of Suffolk’s 35 fire stations sent crews to the scene, with 600 firefighters in total involved in putting out the blaze described as “unprecedented” by the fire chief.
Tristan Gale, Suffolk County Council’s cabinet member for planning, devolution and the fire service, said the move out of major incident arrangements also marked the “beginning of a coordinated recovery phase” led by East Suffolk Council.
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