Winslow announced his candidacy Thursday in a race to fill former Sen. John Kerry's seat, The Boston Globe reported.
Kerry, a Democrat, is now secretary of state.
"I have a proven record of respect for Second Amendment constitutional freedoms," Winslow wrote in an email announcing his candidacy. "My experience as a fiscal conservative and problem-solver is experience we need in Washington, D.C. Our future depends on getting this right."
He said he has committed $100,000 of his own money to begin his campaign and estimates it will cost between $4 million and $6 million to run.
The former judge, who was an aide to Mitt Romney when the 2012 GOP presidential nominee was governor, said he will resign from his law firm, Proskauer, next month, to focus on his campaign.
"I'm going to be 100 percent running for the U.S. Senate," Winslow said. "This is a heavy lift. I'm going to give this race everything I've got."
Other Republicans considering a run for the seat include state Sen. Bruce E. Tarr, former congressional candidate Sean Bielat, private equity investor and former Navy SEAL Gabriel Gomez, and Jon Fetherston, former chairman of the Ashland Board of Selectman, the Globe reported.
Winslow and any other Republican who announces their candidacy will face off in an April 30 primary before the special election to be held June 25.