The 56-year-old, whose most recent job at Hibernian ended in June 2014, is the permanent successor to Justin Edinburgh, who left the club to join League One Gillingham in February, and has signed a two-year deal.
Jimmy Dack had been in caretaker charge but oversaw a run of just five wins from 16 games, including seven defeats.
Butcher, who won 70 caps for England, arrives having previously player-managed Coventry and Sunderland before retiring in 1993, and then managing Motherwell, Sydney FC, Brentford, Inverness and Hibs.
Butcher said: “I’m delighted to be given the opportunity to work for a fantastic club like Newport.
“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.”
County director Howard Greenhaf said: “We were extremely impressed with Terry when we spoke to him. He is very thorough and professional in his approach and we are sure we have the best man for the job.
Butcher will watch County’s final game of the season against Oxford United on Saturday from the stands as Dack continues his work with the team, and will take charge ahead of next season.