Raikkonen, the 2007 world champion, announced on Wednesday he will step away from F1 at the end of the season. The Finnish driver has started more F1 races than any other driver with 341 and is currently in his 19th season in the sport.
Raikkonen made his debut in 2001 and, aside from a two-year sabbatical in 2010 and 2011, has been a mainstay on the F1 grid in the modern era.
The Alfa Romeo driver has two young children and said ahead of Sunday's Dutch Grand Prix he is relishing the prospect of having a free schedule next season in order to spend more time with his family.
When asked if he had plans to race elsewhere, Raikkonen said: "No, no plans.
"I don't want to have some schedule put on, because obviously the last 18, 19 years in F1, since I started, and I did rallying in those two years, there was always a schedule, what is coming next on this date or that date.
"I don't want that. That's for sure one of the big reasons I wanted to do something else, that life doesn't go because of the race or whatever it is, the work that is involved in F1.
"So I'm not in a rush. I've not even thought about it at all yet."
He added: "The schedule can be our family's schedule, and I'm happy with that."
Hamilton has fond memories of competing against Raikkonen, even if he denied the British driver the chance to be a rookie world champion in 2007.
"Kimi was one of the better drivers to go up against," Hamilton said. "He was tough but very, very fair.
"You just knew he was one of the most skillful drivers here. There was a good amount of respect always with him. I know he's got a family, I know he's said he's got things looking forward to enjoying beyond. I just admire his will to continue racing.
"Clearly, racing is in his blood. He will be missed. I remember before I got to F1 being a huge fan of Kimi's. When I played computer games, I'd always be in Kimi's car. So this crazy experience of racing against him, losing a championship to him and then lots of great battles. He will be missed," he added.
Four-time world champion Sebastian Vettel said his time alongside Raikkonen at Ferrari between 2015 and 2018 made him appreciate just how good he was.
"[He is] an incredible talent so seeing that first-hand as a teammate for some years was impressive," Vettel said. "Just the amount of speed he has right from the get-go and the ability to get used to different conditions, different cars.
"He definitely earned his place [in history] and had a long and great career."
When asked what he would miss most about Raikkonen, Vettel made a light-hearted reference to his friend's reputation for being a man of few words, saying: "Silence!"
Raikkonen also had praise from F1's younger generation. Lando Norris, who was born a year-and-a-half before Raikkonen's debut at the 2001 Australian Grand Prix, said Raikkonen was special both on and off the track.
"He is one of the guys that has made Formula One what it is today," Norris said. "From many years ago. He will be missed.
"He is not the big talker, so not be missed by how much he says. But more for the opposite reason.
"He has a lot of character and also not much character the same time. Many people love him because of that. So he will be missed by many, you still one of the best drivers who is been in F1, and he is achieved a lot of things, more than many of us drivers on the grid currently.
"One day I would love to emulate him in a way."