Sandberg signed a three-year contract through 2016 with a club option for 2017.
The Phillies have gone 18-16 under Sandberg since the firing of longtime manager Charlie Manuel on August 16. They had lost 19 of 22 games before Manuel's firing.
Sandberg began the 2013 season as the Phillies third base coach, his first major league coaching position.
This year is his third in the Phillies organization, having served the first two as the manager for triple-A Lehigh Valley, where he went 155-132 (.540) and led the team to their first playoff appearance.
"We are pleased to announce that Ryne Sandberg will be our major league manager," said Amaro. "We feel that Ryne has the qualities and leadership skills that are essential to move our club and our organization forward. Ryne's six years as a minor league manager, Hall of Fame credentials and work ethic warrant this opportunity."
Sandberg is the only Hall of Fame player currently managing in the major leagues and will be the first full-time manager who had a Hall of Fame playing career since Frank Robinson served as the manager of the Expos and Nationals from 2002-06.
He was originally drafted by the Phillies in 1978 and made his major league debut with the team in September of 1981 before being traded to the Cubs. Sandberg played 15 years for Chicago and finished his career with a .285 batting average, 282 home runs and 1,061 RBI in 2,164 games.
ESPN contributed to this report