The retired England batsman was convicted in France in 1998 of hitting his ex-girlfriend; on Tuesday he was unrepentant over the incident, saying that the allegations were untrue and that he "couldn't give a toss" about the criticism.
The opposition Labour party and campaigners called for Boycott's nomination to be rescinded.
"Celebrating a man who was convicted for assaulting his partner sends a dangerous message – that domestic abuse is not taken seriously as a crime," Adina Claire of the charity Women's Aid said in a statement.
Boycott, interviewed on Tuesday after the honour was announced, was irritable when asked about the conviction.
"It’s a cross I have to bear – right or wrong, good or bad, I have to live with it – and I do because I am clear in my mind, and I think most people in England are, that it's not true," Boycott, 78, told BBC radio.
When asked about the charity's criticism, he replied to the female presenter: "I don’t care a toss about her, love. It's 25 years ago. You can take your political nature and do what ever you want with it ... I couldn’t give a toss."
Boycott is set to receive a knighthood after previously expressing his frustration with not getting the honour in terms that also attracted criticism.
In 2017, Boycott apologised "unreservedly" after the Daily Mirror reported that he had said he needed to black up to improve his chances of getting a knighthood given how many West Indian cricketers had received the honour. Boycott said he meant no offence but "what I said was clearly wrong".
Queen Elizabeth grants Resignation Honours at the request of an outgoing prime minister. May nominated Boycott, whose persistence she had vowed to emulate in her ultimately failed efforts to deliver Brexit, among a list of other people.
Boycott scored over 8,000 runs in test cricket and was known for his stubborn and conservative batting style.
"One of my cricket heroes was always Geoffrey Boycott," she said in November when quizzed about how long she would stay in office as ministers quit in protest at her strategy for pulling Britain out of the European Union.
"Geoffrey Boycott stuck to it and he got the runs in the end," said May, who ended up leaving the job in July after repeatedly failing to get her Brexit deal approved by parliament.
May previously mocked her predecessor David Cameron's decision to knight his communications director Craig Oliver, implying that seeing his name on Cameron's resignation honours list had given her a retching feeling.
However, the former Conservative leader has also chosen to honour some of her closest advisers and allies, with her Director of Communications Robbie Gibb, chief Brexit negotiator Olly Robbins, European adviser Peter Storr and de facto deputy David Lidington all receiving knighthoods.
May's former joint chiefs of staff, Fiona Hill and Nick Timothy, the latter an architect of May's approach to Brexit who has been outspoken in criticising his old boss's strategy since he stopped working for her, are in line for lesser honours. Their replacement, Gavin Barwell, has been nominated to sit in Britain's upper chamber, the House of Lords.
Asked about May's choices for honours, new Prime Minister Boris Johnson said: "it is at the discretion of the former prime minister."
"That particular list - definitely a matter for her."
Kim Darroch, Britain's former ambassador to Washington who quit in July after a leak of his memos to a British newspaper prompted a stinging attack from U.S. President Donald Trump, has also been nominated to be made a Lord.
As well as Boycott, May nominated former England cricket captain Andrew Strauss for a knighthood, while Metropolitan Police Commissioner Cressida Dick will receive a damehood.
This story has been published from a wire agency feed without modifications to the text. Only the headline has been changed.