After that date weekly court hearings will take place in High Trees, Chepstow, and administrative work will be transferred to Newport, Hereford and Gloucester.
"The current court accommodation at both Chepstow and Monmouth is of an extremely poor standard, and is expensive to maintain for the low level of business conducted," says the Lord Chancellor's Department.
"Neither court is accessible by people with disabilities, not are there public toilets or telephones, and security is poor."
The department adds the changes should result in an improved service for court users and offer better value for money.
Lord Irvine's decision followed a public consultation process and an in-depth evaluation of the courts by the Court Service, an executive agency of the Lord Chancellor's Department.