The 19 year old, from Donaghmore in County Tyrone, was kidnapped in 1975.
It is the latest in a series of searches carried out by the Independent Commission for the Location of Victims Remains (ICLVR).
It said it was "keen to stress that this is a continuation of the previous operation and not a new piece of work".
The head of the ICLVR's investigation team, Geoff Knupfer, said it was "based on a refinement of information received to date and also on a series of surveys undertaken by ICLVR staff in recent months in the forested area".
Trees are being cleared, and staff and equipment are being assembled at the site on Monday, in expectation that a dig will begin on Tuesday.
It is anticipated that the latest operation will last for approximately 10 to 12 weeks, depending on weather conditions.
A previous search for Mr McVeigh began in Bragan on 23 April, but it drew to a close without success in May.
Prior to that, three searches were carried out in the surrounding area, near Emyvale.
Mr Knupfer said: "The ICLVR hope that this latest search may bring them closer to finding the remains of Mr McVeigh and bring comfort and closure to his long suffering family."
The teenager's mother, Vera McVeigh, who campaigned tirelessly for the return of his body, died five years ago, aged 82.
The Disappeared are those who were abducted, murdered and secretly buried by republicans during the Troubles.
In 1999, the British and Irish governments established the ICLVR in an effort to gain confidential information about the location of their bodies.
Nine bodies have been recovered in searches to date, but seven of the Disappeared remain missing.
The search for the body of IRA murder victim, Columba McVeigh - one of the so-called Disappeared - has resumed in Bragan, County Monaghan.