Former champions Mercedes announced on Thursday that the Briton, who turns 39 next January, would continue with them in 2024 and 2025.
National Football League (NFL) quarter-back Brady, now 46, had a 23-year playing career before finally retiring in February.
“I look at people like Tom Brady, who is such an incredible athlete and has shown what can be done today, so he’s the real role model in that respect I think for all athletes to be able to look at,” Hamilton told reporters at the Italian Grand Prix.
“I’m really, really fortunate that I’ve been able to speak to him to understand as well what he’s done and what he does consistently to keep himself in shape and he’s expressed it in the media anyway.”
Hamilton said double world champion Fernando Alonso, who was his McLaren team mate in his debut 2007 season, was another example.
The Spaniard is still racing at 42 for Aston Martin and remains competitive, finishing second in last weekend’s Dutch Grand Prix. He had two years out after leaving McLaren in 2018 before making a comeback with Alpine in 2021.
“He was here way before I was and took that retirement and came back, and is doing an amazing job,” said Hamilton.
“It just shows that your talent never really leaves you as long as you have that passion and that commitment, you can continue.”
Hamilton said he still had ‘unfinished business’ but made clear it was nothing to do with the controversial 2021 season when he missed out on a record with a late change of the safety car procedures in Abu Dhabi.
That race handed Red Bull’s Max Verstappen, soon to be a triple champion, the first of his titles.
“The unfinished business is getting us back to the top, it’s getting back and fighting for world championships,” said Hamilton.
“It’s been a challenge these past few years.
“On the 2021 thing, I’m not really a revenge person and it’s not about revenge,” added Hamilton. “It’s not about redemption. That’s in the past and there’s nothing you can do about the past.”
Hamilton said his race engineer Peter ‘Bono’ Bonnington would also be continuing to work with him.
“I’m very fortunate and that’s like history as well,” he said. “I don’t think there’s ever been an engineer-driver pairing that’s been this long.”
(Reporting by Alan Baldwin, editing by Toby Davis)