The move was welcomed as a cause for celebration by New Democrat Gerry Rogers.
Rogers, the only openly gay member of the legislature, has been pushing for the change that will ensure transgender people are protected from discrimination under law.
The move is a reversal for the government which had maintained under two different justice ministers that the changes weren't necessary.
King says he stands by his past comments, but acknowledges the legal language has changed across the country.
Once approved, Newfoundland and Labrador will join Ontario, Manitoba, Nova Scotia, and the Northwest Territories to include such language in its legislation.