Mr Sargent, whose brand of ice cream is a household name throughout Lincolnshire and on the north bank, died in Castle Hill Hospital on July 21, aged 52.
He had battled against liver disease and, latterly, cancer.
He and his partner of 16 years, Pauline, were married in the hospital ward just days before he died.
Scores of sympathy cards have been received at the family home and the business in Falklands Way, on the Harrier Road Industrial Estate in Barton.
Sargents owned a number of ice cream parlours in Lincolnshire and in Beverley.
Pauline, 58, said: "It is sad Tony is no longer here to see the rewards of all the hard work he put into the business over the years. It was seven days a week.
"Everyone knew him as the gentle giant. At 22st and 6ft 3in, he was a kind and caring man.
"That has been voiced by lots of people. He just got on with everyone."
Earlier, Pauline had hoped Tony would be strong enough for a wedding ceremony to take place at The Reeds Hotel, Barton.
But due to his poor health, the service was switched to the ward on July 9, where hospital chaplain the Reverend Francis Kissock conducted a wedding ceremony, with family members in attendance.
Pauline said: "It was nice because it was what Tony wanted. It made everything complete.
"It was just sad it was in such dire circumstances.
"We all want to send special thanks to all at ward 33 at Castle Hill Hospital for their caring and kindness, with a special mention to Lee Holland for his continual and constant support."
All the ice-cream outlets will be closed today as a mark of respect.
He is survived by Pauline, his children from a previous marriage, Natalie and Zoe, and his step sons, Michael and Richard.
He was eldest brother to Michael, Ann, David, Barbara, Gary and the late Janet.
The service will be held today from 2pm at Woodlands Crematorium in Scunthorpe. Family flowers only were requested, with donations in lieu for The Lymphona Unit at Castle Hill Hospital to be sent care of Huteson And Sons, 25 Holydyke, Barton-Upon-Humber, DN18 5PR, and cheques payable to Huteson And Sons Charity Account.
For more tributes, visit www.this isgrimsby.co.uk/lastingtribute