On Thursday ahead of the Hungarian Grand Prix, Vettel announced via his new Instagram account that he would be retiring from F1 at the end of the 2022 season.
Both Hamilton and Vettel have been racing in F1 for almost exactly the same time, with the latter making his debut midway through the 2007 campaign that also marked Hamilton's first.
Former title rivals in the late 2010s during Vettel's stint at Ferrari, both drivers in recent years have emerged as the moral leaders of F1 in their calls for societal changes and action on the world's climate crisis.
When asked about how he will remember Vettel as a driver, Hamilton said he was "one of the few people that made it not feel lonely" in F1.
"I kind of knew that it was coming, as there'd been hints, but the realisation of it is another thing," Hamilton said of the Vettel news.
"And I would just say naturally, my first feeling is it's sad to see that he's stopping. And then I have not had a lot of time to think about all the journey that we've gone through together.
"But when I talk about the journey that I've felt I've experienced in this sport, and kind of often feeling that it's been relatively lonely, I would say he's one of the few people that made it not feel lonely.
"He stood by me through a lot of things. I always remember 2007, the press conference in Magny-Cours, and him being very, very outspoken in the driver's briefing.
"And I knew then that he was going to be a powerful figure in the sport. But then seeing his success, and then seeing that he puts others before himself and he's been so brave in speaking out and standing for what he believes in.
"We talk about legends in our sport. I don't really love that name, or that title, to be honest.
"I think he's one of the greatest people that we've seen in the sport. And we need more like him. I'm sad because I will have lost an ally inside the actual sport on the grid.
"But I know that outside, he'll be doing great things. And I hope that we will always remain friends. I hope that there'll be other things that we get to do together outside."
Former Ferrari teammate Charles Leclerc – who revealed Vettel sent him a consoling text following his French GP crash – said it was "sad" to see Vettel retiring, adding: "At least it's sad for me.
"Maybe for him he's much happier in the place he's going now. Obviously, it's going to be strange to not see Seb inside the paddock.
"I've learned so much driving with him, and he's always been super-nice to me.
"I'll definitely miss having Seb in the paddock, but I wish him the best and I'm sure he will find other things that will make him happy in another way."
Red Bull's Sergio Perez, who was replaced by Vettel at Aston Martin for the 2021 season, expressed "pride" in the German's achievements and sympathised with his reasoning for retiring.
"I feel very proud of Seb, of what he has achieved," Perez said. "He's a great legend of the sport, he's a great guy. He's always been very fair, very vocal, he's been very successful, has a beautiful family.
"He has everything you'd hope for a colleague to achieve. So, I'm very proud of him and wish the best to him and his family.
"I think that's a very personal decision. I think that's extremely personal, it's how you feel and what you want to do and how your family is.
"When you get older you definitely put other priorities in place, and then you are not willing to pay the price of being an F1 driver because it has a price.
"Sometimes you are and sometimes you are not."
Perez's Red Bull teammate Max Verstappen says Vettel is "a great ambassador" for F1, but feels it is "important" he can now "enjoy his life".
"I mean, at the end of the day, he has achieved so much in this sport, that it's fully understandable for him to retire," the reigning world champion said.
"I mean, I think he's had an amazing career. He's won a lot of races; he's won a lot of championships as well.
"And I think of course, he's a great ambassador for the sport. So, you know, to see him go is… it's something that you can see coming, everyone is getting older, at one point, everyone is retiring.
"And is of course, never nice when that moment arrives, especially, of course, for Seb's fans. But these things happen.
"And I think it's important now that he's just going to enjoy his life with the family, because F1 is such a short period of time in your life that you work so hard to achieve all these things he has achieved and now it's time to enjoy."
Fernando Alonso, who fought with Vettel for the world title in 2010 and 2012 – losing out to the German on both occasions – labelled him as one of his strongest F1 rivals alongside Hamilton and Michael Schumacher.
"Lewis and Sebastian, both of them probably I share most of my time here," Alonso said.
"Obviously, Michael will remain always maybe my top pick, because, you know, I was fighting for the championship with him and I grew up watching him in Formula 1, dominating the sport.
"So, I learned so many things from Michael. And then with Lewis and Seb, yeah, the three of us we shared a lot.
"We will miss him after so many years, you know, sharing the track together with fights, obviously.
"His championships, I was somehow in there as well. So yeah, [he's a] great champion.
"Also a great man, with very strong values and lovely family and probably that decision also this, as I heard the family, so wishing him the best, and hopefully, he's around in the paddock."
Additional reporting by Adam Cooper, Jonathan Noble and Luke Smith
