Interim manager Rangnick has until the end of the season to make his mark at Old Trafford, with scope for two further years as a consultant, after club legend Ole Gunnar Solskjaer was sacked in late November.
Former RB Leipzig head coach Rangnick started with a 1-0 home triumph over Crystal Palace on Monday (AEDT), becoming the first German boss to win his opening game in the Premier League after five countrymen previously tried and failed.
United technical director Darren Fletcher and coach Kieran McKenna acted as assistants for that victory and Rangnick has now bolstered his backroom staff with new appointments.
Lense has worked alongside Rangnick previously, most recently at RB Leipzig, while United's new boss got to know former New York Red Bulls manager Armas while operating as Red Bull's global head of sport and development.
"It won't be that many [staff coming in]," Rangnick said. "So far I'm very happy to work with the staff I have met last week, and they gave me a lot of help in the last couple of days in preparation for the Crystal Palace game.
"We have decided to bring in a sports psychologist, with Sascha Lense. He's from Germany, he's a former second division player.
"I worked with him for three years at Leipzig, in the year I won promotion from the second to the first division myself and the following two years when Ralph Hasenhuttl was head coach and Zsolt Low – the current assistant coach of Thomas Tuchel [at Chelsea] – was assistant coach.
"I will also have one other assistant coach, with Chris Armas. Chris used to be the assistant coach at the New York Red Bulls under Jesse Marsch. That was five years ago, when I first met him. Since then, we have met quite frequently."
With United's spot in the next round of the Champions League already confirmed, Rangnick has hinted at heavy rotation for Wednesday's home clash with Young Boys, who have not won away in the Champions League or European Cup since August 1960.
The 63-year-old Rangnick confirmed that Donny van de Beek and Dean Henderson will start and told the club's official website that Nemanja Matic will captain the side.