Galvis, 28, is slated to become a free agent following the season. He played in all 162 games last season and batted .255 with 12 homers and 61 RBIs last season.
The top-notch defender committed just seven errors last season and eight in 2016.
Philadelphia was looking to move Galvis to open up a starting position for top prospect J.P. Crawford.
San Diego was seeking a shortstop because highly regarded Fernando Tatis Jr. is believed to be one year away from reaching the majors.
Galvis has a .245 average with 52 homers, 233 RBIs and 43 steals in parts of six seasons with the Phillies. He was the starting shortstop each of the past three seasons.
The right-handed De Los Santos went 10-6 with a 3.78 ERA in 26 appearances (24 starts) at Double-A San Antonio last season. He turns 22 on Christmas Day.
San Diego cleared a 40-man roster spot for Galvis by designating right-hander Jose Ruiz for assignment. The former catcher went 1-2 with a 5.98 ERA in 44 appearances at Class A Lake Elsinore last season.