England have not won a major trophy since the 1966 World Cup.
They will start their qualification process for the 2026 tournament in Canada, Mexico and the United States next year.
The FA approached Manchester City manager Pep Guardiola in the summer to see if had an interest in the role, while Newcastle United boss Eddie Howe and ex-Brighton and Chelsea manager Graham Potter were also linked with the position.
FA said, external Tuchel was the “preferred candidate” from “several” managers interviewed.
It said the FA board approved the decision last week and Tuchel signed a contract on 8 October.
Under Carsley, England lost to Greece on 10 October and beat Finland on 13 October.
“The announcement was delayed to minimise distraction around the international camp that has just concluded,” an FA statement read.
English coach Anthony Barry, who worked with Tuchel at Chelsea and Bayern, will be his assistant.
Tuchel won the German Cup with Borussia Dortmund and two Ligue 1 titles at Paris St-Germain, including a domestic treble in 2019-20.
He became Chelsea manager in January 2021, winning the Champions League, Club World Cup and Uefa Super Cup before being sacked in September 2022.
After Bayern failed to win the Bundesliga title last season for the first time since 2011-12, Tuchel left despite still having a year to run on his contract.
“Exciting times for England, with a generation of talented players and a new manager taking the reins,” the Prince of Wales said, external on social media.
“Thomas, wishing you the best of luck, we’re all behind you! W”
Carsley will return to manage England Under-21s when Tuchel takes over.