Valbona Lucaj and husband Sebastiano Quagliata signed the agreement with Lapeer County authorities on the same day they appeared in court on charges related to the death of Craig Sytsma, 46, of Livonia.
He was attacked by two cane corsos on July 23 in Metamora Township, 45 miles northwest of Detroit. The agreement says the dogs and a third cane corso will be killed as soon as possible.
The dogs have been in custody along with eight puppies. The puppies will be offered to an animal rescue group.
Meanwhile, bond was set at $500,000 each for Lucaj and Quagliata, although prosecutors wanted $1 million, saying they might flee the country. Magistrate Mike Delling settled on a lower amount but noted there's "some question" about the couple's status in the U.S.
It wasn't immediately known if the couple could pay the bond and get out of jail or arrange payment through a bond agency. Messages seeking comment were left for their attorneys.
"It's a horrible tragedy ... but animal cases get a lot of attention," assistant prosecutor Michael Hodges said outside court.
He said an "extensive history" of previous attacks by the dogs had a role in the charges, which include possessing a dangerous animal causing death.
Lucaj, 44, a native of Albania, and Quagliata, 45, a native of Italy, have had a long-running legal battle with federal immigration officials after arriving here in the late 1990s.
Lucaj was named, but not charged, in a bribery scandal involving an immigration official in New York. The government said she and other immigrants paid a middleman to ensure they would be granted asylum.
The government in 2010 took some steps toward deporting Lucaj and Quagliata, but legal challenges have stalled the process, court records show. In March, a federal judge in Detroit declined to overturn a decision rejecting the couple's application for naturalization.
"Given the posture of their immigration cases, ICE has not yet initiated removal proceedings against either individual," said Khaalid Walls, a Detroit spokesman for U.S. Immigration and Customs Enforcement, known as ICE. "ICE will, however, continue to closely monitor the matter and take appropriate enforcement action once the local criminal proceedings are resolved."
Lucaj and Quagliata return to court on Aug. 8.
Murder charges against dog owners are rare. In May 2013, a man was charged after a 63-year-old woman died from more than 150 bites by four pit bulls in California's Los Angeles County. The case against Alex Jackson is pending.