The entertainer, who spent the final months of his life raising funds for cancer research, gained 36,936 of the total of 130,560 votes cast by Today listeners.
Fiona Castle said her husband, best known as presenter of Record Breakers on BBC Television, would have been stunned by the award.
"I think he would have been the most amazed person of all because he actually had quite low self-esteem," she said. "He never imagined that people loved him as much as they did."
John Major surprised critics by coming in second, with 27,838 votes. He beat the Labour leader, Tony Blair, who was fourth.
Listeners cited the Prime Minister's role in the Northern Ireland peace process as the main reason for their vote, but Labour Party officials suspect Conservative Central Office rigged the result. "This clearly is not representative of the view of the population at the moment," a spokesman said. "It is normal Conservative Central office practice to get members to ring in with votes. They have a "telephone tree" - like a chain of people calling each other - and I assume that is what they have been doing this time."
This is the first year that the Today programme has allowed listeners to cast votes by telephone. The numbers are published on Ceefax and there are no safeguards preventing multiple votes being cast.
"We couldn't tell who the callers were," a Today spokesman said. "We were astounded by the number of people who rang. In 1990, we got just over 1,000 votes; this year we got over 130,000."
The South African President, Nelson Mandela, came third; Teresa Gorman, the Euro-rebel MP, was fifth and John Hume, leader of the Social Democratic and Labour Party, came sixth.
The contest - formerly the Man and Woman of the Year title - was suspended four years ago after ballot-rigging allegations.
In 1990, Lai Krishan Advani, leader of India's Hindu Bharatiya Janata Party, was disqualified after several identical letters proposing him were found.
Many people also claimed that Margaret Thatcher's repeated success - she won the female award eight of the nine years the contest was run - was due to orchestrated campaigns by Young Conservatives.
But Conservative Central Office denied that this year it had encouraged members to vote for Mr Major, accusing Labour of "sour grapes".Reuse content