King joins Manchester United after eight years at Burnley, where he held a succession of coaching positions after ending his playing career.
The 27-year-old came through Burnley's academy after joining the club at the age of 11 and represented England at Under-16 level. He subsequently moved into coaching, working across Burnley's youth and senior teams before taking responsibility for goalkeeping at first-team level.
He will work under Craig Mawson, United's lead first-team goalkeeping coach, as Carrick continues to assemble his coaching structure following his appointment.
United confirmed King's arrival on Thursday, with the club describing his previous work at Burnley as the basis for his move to Old Trafford.
King's addition gives Mawson another specialist within the goalkeeping department and completes another piece of Carrick's backroom staff.
The former goalkeeper has effectively spent most of his professional life at Burnley. After progressing through the academy and receiving international recognition as a teenager, he decided to move into coaching rather than pursue a lengthy playing career.
His coaching education began within the Burnley system in 2018, initially working with younger players before moving progressively closer to the first team. Transfermarkt records spells with the club's youth, Under-23 and senior sides during that period.
King also gained experience around the first team during Burnley's managerial changes, including working with several senior coaches.
His arrival comes at a difficult point for United. Carrick's side have collected five points from their opening five Premier League matches, with the latest result a 1-1 draw at Fulham.
The club's goalkeeping department has nevertheless remained an area of continuity during the coaching changes. Mawson stayed on after Ruben Amorim's departure and will now work alongside King.
United have subsequently confirmed the wider structure around Carrick, with Steve Holland, Jonathan Woodgate, Jonny Evans and Travis Binnion also part of the first-team coaching group.
For King, the move represents a major step from developing goalkeepers at Burnley to working within one of English football's biggest first-team environments.