"Today is your last dance. You, who have given us so much. We should have given you a better ending, but we failed," the 27-year-old forward wrote in a message shared on social media before Les Bleus take on England in the third-place match later on Saturday.
Deschamps, who took over in 2012, led France to the 2018 World Cup title and another final four years later before their 2026 campaign ended in a semi-final defeat by Spain.
"Putting into words what you have brought over 14 years is very difficult, because you have been such a major figure in the rebirth of this team," Mbappe said.
"People have not always known how to appreciate your greatness, but time and history will take care of that."
Mbappe, France's all-time leading scorer with 64 goals, also thanked Deschamps, the team's captain when France won the 1998 World Cup, for giving him the opportunity to represent his country on the biggest stage.
"I feel privileged to have been alongside one of the greatest legends of our country," he said. "I will only keep great memories of everything we experienced and achieved together.
"I wish you all the best in your new adventure."
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FIFA World Cup 2026 final
The 2026 FIFA World Cup final will take place at the MetLife Stadium in New Jersey on Sunday, July 19th, with kick-off at 21:00 CET. Defending champions Argentina and European champions Spain are set to go head-to-head for football's biggest prize.
World Cup final: All you need to know | Full World Cup schedule | Knockout bracket | How to watch the World Cup | World Cup Format | Past winners of the tournament