Neil Entwistle, who was arrested in London on Thursday, will not contest extradition and wishes to return to the United States "as soon as possible," his attorney, Dan Brandon, said at Bow Street Magistrates Court.
That could be within the next week, reports CBS News' Vicki Barker.
District Judge Anthony Evans told Entwistle that his decision to voluntarily return would be irrevocable.
"Yes, that's right," Entwistle replied. He glanced briefly at his father, Cliff Entwistle, as he signed a form consenting to return. There was no immediate indication when Entwistle would leave Britain.
Entwistle is accused of fatally shooting Rachel Entwistle, 27, and 9-month-old, Lillian, on Jan. 20.
In Massachusetts, Middlesex District Attorney Martha Coakley told reporters Thursday that an arrest warrant was issued after forensic results indicated the .22-caliber handgun used in the killings was from a collection owned by Entwistle's father-in-law.
Massachusetts authorities flew to London late last month to interview Entwistle at the U.S. Embassy, but officials didn't say whether he answered any questions then, Christina Hager of CBS station WBZ-TV in Boston reported. He was considered "a person of interest" at the time, not officially a suspect, and had been staying at his family home in Worksop, in central England.
Prosecutors believe Entwistle took the gun from his father-in-law's home, then secretly returned it after the slayings.
Authorities allege Entwistle shot his wife in the head and his daughter in the abdomen as they lay together in bed. The district attorney said it was unclear whether the two were awake or sleeping at the time.
The next day, Entwistle flew to London, authorities said.
A first-degree murder conviction in Massachusetts carries a mandatory sentence of life in prison without parole.
Coakley said Entwistle's finances had deteriorated after the failure of his Internet businesses, which included a Web site that promised customers as much as $6,000 in monthly earnings and another that offered a manual to help men enlarge their penises.
Entwistle had met Rachel Souza, an American, in 1999 at the University of York in England, where she was spending a year abroad. They were married in 2003 and later moved to the United States.