The contract with Hódút is expected to be signed later in 2022, NIF said.
The 32.2 km stretch of the M44 will run between Kecskemét and Szentkirály.
Close to 90 km of the M44, between Lakitelek and Békéscsaba, has already been completed.
Tamás Herczeg, an MP for the region, said in Tuesday's issue of daily Békés Megyei Hírlap that motorists could expect to travel the entire distance between Békéscsaba and the capital on dual carriageways from 2025.