The union has now accepted assurances from employers that there would be no compulsory redundancies arising from the transfers.
The RMT has also been assured that the TUPE transfer of undertaking rules would apply to all staff.
Last week the RMT called a strike ballot of Jarvis staff after it was claimed that Network Rail had repeatedly failed to provide an assurance that there would be no compulsory redundancies or worsened conditions.
Bob Crow, general secretary of the RMT, said: "Following consultations with members around the country, the executive has accepted assurances from Jarvis and Network Rail that no compulsory redundancies or worsening of conditions will result from these transfers."
A dispute with First Engineering has also been settled after similar assurances were received.