Midfielder Afumuzor arrives from Portsmouth, while defender Yeutembip is signed from Charlton Athletic and Mukumbira joins from Peterborough.
All three U15 players have announced their Newcastle move on social media.
Newcastle can now sign players of such age groups nationally after developing a full-time training model for youth levels.
Previously, Newcastle could only add players who lived within an hour-and-a-half of the club's academy base.