Amla joins from IBM and will start on Dec. 1, Capita said.
He will focus on changing Capita's sales model, the company said.
Two weeks ago Capita hired a new chief financial officer, Patrick Butcher, from bus and rail operator Go-Ahead Group.
CEO Lewis was appointed late last year after a series of profit warnings which prompted the company to raise 700 million pounds ($893 million) in April.
Capita reported a 60 percent fall in half-year pre-tax profit in August.
Like peer Carillion, which collapsed at the start of this year, Capita depends on a mix of public and private contracts, although it is focussed chiefly on IT services.
Amla's appointment confirmed a Sky News report http://bit.ly/2wNQxlI.
(Reporting by Justin George Varghese in Bengaluru; editing by David Evans and Jason Neely)