He succeeds Justin Edinburgh who left for Gillingham in February. Caretaker boss Jimmy Dack will oversee Saturday's match at home against Oxford United.
"I'm delighted to be given the opportunity to work for a fantastic club like Newport County AFC," Butcher told the club's website.
"I have met a lot of great people at the club already and have seen the passionate fans for myself at recent games.
"I look forward to the new challenge and I'm looking forward to working together with everyone at a club that has great aspirations for the future."
Former Ipswich Town and Rangers defender Butcher has been out of work since being sacked as manager of Hibernian in June 2014.
His managerial CV also includes spells with Coventry, Sunderland, Motherwell, Brentford, Sydney and Inverness Caledonian Thistle and.
He takes over a County side set for a third season in League Two after being promoted from the Conference Premier in 2013.
They are three points outside the play-off places with one game remaining, but their inferior goal difference means they are unlikely to overtake seventh-placed Plymouth.
County director Howard Greenhaf said the board were "extremely impressed" with Butcher when they spoke to him.
"He is very thorough and professional in his approach and we are sure we have the best man for the job," said Greenhaf.
"As soon as Terry was connected to the job he came and watched us himself several times and also sent people to our games on his behalf.
"He already knows the team in good detail and has firm plans on what he wants for next season."