The Englishman revealed to the publication that he met Clare, 54, eight years ago when he was starting out on tour.
Clare was a sports agent and set out to try and poach him for the company she worked for. The couple fell in love and married in the Bahamas in 2017.
The couple have a son, called Franklin. He was born not long after they tied the knot. Fleetwood also has two stepsons aged 14 and 16.
Asked if he gets tired of people raising their eyebrows at the age gap, Fleetwood told the publication:
"Oh, we definitely get comments. But it's never been a thing to us. Clare actually looks very young for her age and I look old — it's probably all that sun. She's incredibly cool and I'm not cool at all, though I am quite mature for my age."
If the roles were reversed, Fleetwood said nobody would bat an eyelid.
"We planned to keep our life and our work separate, for me to find another agent. But it became more apparent I wasn't going to find anybody I'd trust as much because, after all, Clare is a very, very, very good agent by trade; it wasn't like she was my wife just helping the family out.
"So in the end we thought, 'We'll just give it a go, but we will never let anything get in the way of our relationship,' and it's just always worked perfectly."
Last July, Fleetwood confirmed that his mother had died aged 60 after being diagnosed with cancer.
It was days after he competed at the 150th Open Championship at St. Andrews.
Of this, Fleetwood told the Times "it stinks", adding:
"Mum was far too young to go and I was far too young to lose a parent. She was the only person, apart from Clare, who texted me every day.
"She'd been poorly for a decent stretch of time — two or three years in and out of hospital and on and off chemo — so I'd already been mourning in my own way, but obviously you never expect someone to die.
"Going through something as painful as this definitely makes you more tender to other people, but you deal with the hand you've been dealt and become a better person from it."
He added:
"My parents always travelled with me, so people were always asking why she wasn’t on the tour and, 'How's your mum and dad?' But I didn't want to say, 'Actually, she has cancer, she's really struggling,' because that would stop them in their tracks and they wouldn't know how to answer and I didn't want to ruin anybody's day.
"I'd never want anyone to feel they had to console me when they might be dealing with their own stuff.
"Plus, I didn't know if my mum and dad wanted people to know, so it was just best to keep it quiet.
"When you lose someone you just need to remember them in the right way and then enjoy the time with the people who are still there. It's all brought me even closer to Clare."