The former United States midfielder, who worked under Ralf Rangnick at Manchester United, will team up with countryman Jesse Marsch's backroom staff at Elland Road, subject to obtaining a work permit.
Marsch said: "I'm delighted to welcome Chris to Leeds United. He will be a fantastic addition to the staff.
"He brings a wealth of experience from across the world and, having worked closely with him previously, I am sure he will help us to improve every day."
Armas, 50, was Marsch's assistant at New York Red Bulls from 2015-18 before becoming head coach when the latter departed to RB Leipzig, and also had a spell in charge of Toronto FC.
He teamed up with Rangnick at Old Trafford in December 2021 and left at the end of the 2021-22 season before Erik ten Hag took over.
Armas, who spent his playing career at the Los Angeles Galaxy and Chicago Fire and made 66 appearances for the USA, is expected to be in the dugout for Leeds' FA Cup fourth-round tie at Accrington on Saturday.