Baumel was a tank driver.
Israel has negotiated for the repatriation of their bodies for decades.
The U.S. -born Baumel immigrated to Israel along with his parents in 1970. It was not repatriated as part of a deal with any other country.
Israeli Prime Minister Benjamin Netanyahu, in his eulogy for Baumel at a military cemetary in Jerusalem, thanked Russian President Vladimir Putin for his help.
But an Israeli newspaper reported past year that their bodies were believed to be buried in the Palestinian refugee camp of Yarmouk, in southern Damascus, which Syrian troops recaptured from Islamic State (IS) militants that May. "For all those years, the State of Israel had invested vast resources to resolve the riddle of his fate".
"And today, when we bring you, Sergeant First Class Zachary Baumel, to eternal rest, almost four decades after you fell, is the day that the State of Israel fulfills the oath it makes with its soldiers, men and women", he added.
In 2016, an Israeli tank from the war was returned to Israel by Russian Federation.
In one high-profile case, the families of two soldiers killed in Israel's 2014 war in the Gaza Strip have pressed the government to bring back their remains, believed to be held by Hamas.
The identification was also verified by IDF Chief Rabbi Eyal Karim.
Jonathan Conricus, an Israeli military spokesman, said Wednesday that the remains of Zachary Baumel had been returned to Israel and identified after almost four decades of intelligence operations. "Russian Army soldiers found the body in coordination with the Syrian military", he said. "As Zachary's former congressman, I spoke from the House floor and worked closely with his family, and in conjunction with several organizations, in pursuit of justice and answers regarding the condition of Zachary and his fellow soldiers". He was one of three IDF soldiers whose bodies were found in the aftermath of the tank battle. "We will not cease until all our soldiers have returned home".
Two other Israeli tank crew members are still listed by the military as missing in action from the June 10-11, 1982 battle. Our commitment to our soldiers has always been, and will always be, a shining light. "We hope and pray that all the remaining missing will be returned home to their rightful places in the land of Israel". He attended a hesder yeshiva, which combines religious study with army service.
Baumel's parents, NY natives who moved in Jerusalem, launched a years-long search and rescue campaign to find their son. He recalled the pain of his late father, who "traveled the world to track down any peace of information about his missing son".
The last postcard Zachary Baumel sent to his family before going missing in Lebanon read "Don't worry, everything is OK, but it looks like I won't be home for a while".