The German, who's managed Chelsea, Paris St Germain and Bayern Munich, becomes the third non-Englishman to hold the post after Sven-Goran Eriksson and Fabio Capello.
The 51-year-old, who will be assisted by English coach Anthony Barry, will take up the role on January 1 ahead of the World Cup qualifying campaign after signing an 18-month deal.
At a Wembley press conference, Tuchel said: "I'm obviously very excited and honoured to be here today as the new head coach of England.
"I want to take the opportunity to thank the FA for their trust and I am very excited to start this journey in January with a very special and exciting group of players to make our dream come true in America.
"I understood very quickly that is it is a big job, I think always the job you are in is the biggest job and it makes no sense to compare, but it feels big and feels like a privilege."
Bavaria-born Tuchel also addressed the critics who believe an Englishman should lead the national team and offered words of reassurance.
"I'm sorry, I have a German passport," he added. "All of those supporters maybe felt my passion for the English Premier League and the country and how I love to live and work here.
"Hopefully I can convince them and show them and prove to them I am proud to be an English manager and do everything to show respect to this role and this country and the target for the next 18 months."
Tuchel moved into coaching after his playing career was cut short by a knee injury, working at Stuttgart, Augsburg and Mainz before succeeding Jurgen Klopp at Borussia Dortmund in 2015.
He moved on to PSG two years later, winning successive Ligue 1 titles, then joined Chelsea in January 2021, guiding them to the Champions League crown a few months later.
He was dismissed in September 2022 amid claims of a breakdown in relations with the club's hierarchy and was out of work until joining Bayern Munich in March 2023.
He secured the Bundesliga title that season but last term was something of a disaster, with Bayern failing to win a trophy, and Tuchel's impending departure announced in February.
He admits the prospect of moving from club football to the international game is something he is relishing.
"It is very new because I come from club football but the new role is also very exciting," he said.
