Rasmea Odeh, 69, will be deported to Jordan or another country in the months ahead.
Supporters traveled to Detroit from Chicago to pack the courtroom, and many were in tears later on the courthouse steps.
Odeh was convicted at trial in 2014 and sentenced to 18 months in prison, but the verdict was overturned. A second trial was planned in Detroit, the city where she went through the citizenship process in 2004, before she decided to accept a plea deal.
But even with the plea agreement, Odeh found it impossible to say the word "guilty" when repeatedly asked by US District Judge Gershwin Drain. He gave up and accepted her reply that she had admitted her crime in the court document.
"I signed this," Odeh said.
She won't spend any time in prison and will wait for US immigration officials to tell her when she must leave the country. The deportation won't happen until after she appears in court in August.
"The United States will never be a safe haven for individuals seeking to distance themselves from their pasts," said Steve Francis, special agent in charge of Homeland Security investigations in Detroit.
In 1970, Odeh was convicted of two bombings in Israel, including one that killed two young men at a supermarket in Jerusalem. She insists she was tortured into confessing. She was sentenced to life in prison but was released in 1979 as part of a prisoner swap with the Popular Front for the Liberation of Palestine.
With family in Michigan, she applied for a US visa in 1994, but didn't disclose her criminal record. She also didn't disclose it when she applied for citizenship in 2004. Her record would have disqualified her from entering the US.
In the plea agreement with prosecutors, Odeh said she made the false statements "intentionally and not as a result of any mistake, post-traumatic stress disorder or any other psychological issue or condition or for any innocent reason."
In Chicago, Odeh has worked as associate director of the Arab American Action Network, which provides social services and education. She is widely respected for her work with immigrants, especially Arab women.
Hatem Abudayyeh, director of the organization, told Odeh's allies outside the courthouse that she's guilty only of "dedicating over 50 years of her life to the liberation of Palestine."
Before the guilty plea, a Detroit-area man held a sign outside to honor Leon Kanner and Eddie Joffe, the victims of the 1969 supermarket bombing.
"I'm out here for the families," Dan Cutler, 65, said.