The violin vanished from Totenberg's office in 1980 while he was greeting well-wishers after a concert.
The instrument surfaced in June when a woman had it appraised after inheriting it from her husband.  It was immediately reported to authorities.
Violins created by Antonio Stradivari are considered amongst the world's finest and can be worth millions.
Totenberg was a child prodigy in his native Poland and bought the instrument in 1943 for $15,000 (Â£9,675) - more than $200,000 (Â£129,000) today.
It was the only instrument he performed with until it was stolen, though he continued performing into his 90s.
However, he did not live to see the recovery of his beloved violin, dying at the age of 101 in 2012.
His daughter Nina, instead, was alerted to the news by an FBI agent.
"I really could hardly believe it at the time," said Totenberg, who is the legal affairs correspondent for US radio network NPR.
"I said, 'I have to call my sisters. I'll tell them not to get their hopes up' but (the agent) said, 'You don't have to do that. This is the violin.'"
"This loss for my father was, as he said when it happened, it was like losing an arm," added daughter Jill Totenberg, a public relations executive in New York.
"To have it come back, three years after he died, to us, it's like having him come alive again."
The violin was in the possession of the former wife of Philip S Johnson, who died in 2011.
Johnson's obituary described him as "a noted violinist of 40 years". Totenberg said he had been around her father's office at the time of the instrument's disappearance.
Prosecutors do not plan to charge anyone in connection with the theft.
The violin will be returned to the Totenberg family, who are planning on selling it to a performer.
"I'm just glad that the violin, once it's restored to its full potential again, will eventually be in the hands of another great artist and its gorgeous voice will be heard in concert halls around the country," said Nina Totenberg.
A Stradivarius belonging to violin virtuoso Roman Totenberg has been recovered, 35 years after it vanished.