The German was assisted by technical director Darren Fletcher and first-team coach Kieran McKenna during his first match in charge – Sunday's 1-0 victory over Crystal Palace.
Both were present during Ole Gunnar Solskjaer's managerial reign, but the coaching staff numbers were reduced when Michael Carrick announced he was leaving the club after last week's 3-2 win over Arsenal.
With that in mind, Rangnick has moved to further bolster the ranks, by recruiting coach Chris Armas and sports psychologist Sascha Lense.
Armas is a former New York Red Bulls and Toronto FC manager, and enjoyed a long playing career in Major League Soccer and with the US national team.