The ex-Crystal Palzace, Energie Cottbus and 1860 Munich defender will finish up at the end of the MLS regular season and Beckham has praised him for his contributions to the Galaxy cause over the last few years.
"It's been an honor to be on the same team as Gregg. He's such a great professional, a great leader," Beckham said.
"And, he's that person that when the team is not playing as well as we should be, he's the one that's giving the information and giving all of us a kick on the backside.
"It's great to have a professional like that in the team. Sad to see him finishing now, but he went out on a high, winning tonight against our rivals, he's had such a great career and he deserves some well needed time with his family now."