Relatives of Dr. David Sinclair told The Associated Press that they were "blown away" and "honored."
So-called "birthers" have questioned Obama's birthplace, espousing theories that he was not born in the U.S., possibly his father's native Kenya, and therefore ineligible to be president.
Obama released a short form copy of his birth certificate in 2008. Recently, potential Republican presidential candidate Donald Trump began questioning why he hadn't ensured that the original certificate was released.
On Wednesday, the White House released a copy of the original birth certificate.
Below Obama's mother's signature was one which appeared to read: "David. A. Sinclair."
Sinclair had an obstetrics and gynecology practice in Honolulu and delivered babies all over Hawaii when Obama was born in 1961, said his son Karl Sinclair, 55, of Kailua. The doctor retired in the late 1990s and died in 2003 at 81.
"What a shocker," said Karl Sinclair, one of six children. "It's amazing. I'm blown away by it, quite honestly."
They found out because one of their relatives was awake at 3 a.m. watching the news and saw the signature, said Dawn Yoshimura-Sinclair, who is married to another Sinclair son, Dr. Brian Sinclair, a neuroradiologist.
"We can attest to the fact that it is indeed dad's signature," Yoshimura-Sinclair said. "It's not a common name over here. There's no confusion that it was dad."
Relatives said while they previously never made the connection, looking back it makes sense because there were few obstetricians in Honolulu at the time.
"He never turned anyone away," said Karl Sinclair's wife, Julie Sinclair. "Whether they could pay or not."
Born in Portland, Ore., the doctor joined the military after the Pearl Harbor bombing, relatives said. He went to the University of Hawaii after the war.
He then went to medical school at the University of California at San Francisco, where he completed his residency.
Sinclair returned to Honolulu with his wife and children in 1960. He delivered babies mostly at what is now known as Kapiolani Medical Center for Women & Children, where Obama was born.
The doctor never spoke about his patients, his children said, but they imagine his father would be thrilled one of the babies he delivered grew up to be president.
"I'm just honored and proud of my father," Karl Sinclair said.
"I think it's great," said Dr. Brian Sinclair, who pursued a career in medicine because of his father. "Hawaii was a very small place back then so I guess I'm not surprised."
Brian Sinclair graduated from the same high school as Obama but didn't know him personally. The Sinclair family includes Obama supporters and those who didn't vote for him, they said.
Karl Sinclair said he hopes the birth certificate will end the speculation.
"To me, the birth certificate doesn't lie," he said. "I think that should put everything to bed."