In 2016, Ray Mabus, the secretary of the Navy, announced the ship would be named after Mr. Milk.
“Naming this ship after Harvey Milk is a fitting tribute to a man who had been at the forefront of advocating for civil and human rights,” Mr. Mabus said at the time.
The ship will have a crew of 125, Lt. Tim Pietrack, a Navy spokesman, said.
The naming of the ship in Mr. Milk’s honor has been in the works for several years. In 2012, the San Francisco board of supervisors passed a resolution requesting that Mr. Mabus name a ship for Mr. Milk, who had followed family tradition in joining the Navy.
Mr. Milk enlisted at a time when the military barred gay, lesbians and bisexual people from serving. Military members believed to be gay were harassed, questioned and given dishonorable charges. In 1955, Mr. Milk was discharged with the rank of lieutenant junior grade, according to the Navy.
Mr. Milk moved to San Francisco, where he opened a camera shop and became a leader in the gay community. He was known for using a bullhorn to rally crowds. Less than a year after being elected to the board of supervisors in 1977, he was fatally shot by his former city supervisor opponent, Dan White.
Mr. Milk’s legacy has been celebrated in books, an opera and even a postage stamp. His story was chronicled in the 2008 movie “Milk’’ starring Sean Penn. There was also a documentary in 1984, “The Times of Harvey Milk.” In 2009, President Obama posthumously honored Mr. Milk with the Presidential Medal of Freedom.
Mr. Milk’s nephew is the executive chairman of the Harvey Milk Foundation, which is based in South Florida. He said he was looking forward to seeing the ship when it’s completed in about 18 to 24 months.
“I really think it sends an important message,’’ he said. “We will celebrate everyone.”