Philadelphia also activated infielder Jean Segura from the 60-day injured list and right-hander Kyle Gibson from the bereavement list.
The 32-year-old Gregorius is batting .210 with a homer and 19 RBIs in 63 games this season. He agreed to a $14 million, one-year contract with Philadelphia in December 2019, and then hit .284 with 10 homers and 40 RBIs in his first season with the Phillies.
He agreed to a $28 million, two-year contract with Philadelphia in January 2021.
Gregorius broke into the majors with Cincinnati in 2012 and also played for Arizona and the New York Yankees before moving to Philadelphia. He is a .257 hitter with 134 homers and 530 RBIs in 11 years in the majors.
Segura, 32, had been sidelined by a broken right index finger. The two-time All-Star appeared in eight rehab games for Triple-A Lehigh Valley, going 6 for 30 with six walks.
In partnership with NBC Sports Philadelphia
Syndergaard is slated to start Thursday night against the last-place Nationals. The Phillies sent outfielders Mickey Moniak and Jadiel Sánchez to the Angels for Syndergaard, who is 5-8 with a 3.83 ERA in 15 starts this year.
Marsh, 24, also came over from the Angels in a separate trade for catching prospect Logan O’Hoppe. Marsh batted .226 with eight homers and 37 RBIs in 93 games with Los Angeles this year.