Both Sky Sports News, the BBC and other British outlets have reported the German agreed a deal on Tuesday.
England's Football Association is holding a news conference at Wembley on Wednesday with chief executive Mark Bullingham.
Tuchel, 51, is set to become the third foreign manager to take charge of the England men's team, after Sweden's Sven-Goran Eriksson and Italian Fabio Capello.
Tuchel, who led Chelsea to the Champions League title in 2021, will replace caretaker Lee Carsley, but some reports suggest the interim coach will remain in charge until after the November Nations League matches.
England have been seeking a permanent manager since Gareth Southgate resigned following England's defeat by Spain in the European Championship final in July.
Tuchel has been out of work since leaving Bayern at the end of last season after the German giants finished third in the Bundesliga, behind Bayer Leverkusen and VfB Stuttgart.
After injury forced him to retire early as a player Tuchel did bar work while studying and coaching at youth levels before becoming coach of Augsburg reserves.
He built his reputation as a forward-thinking tactician in the Bundesliga after taking over from Jurgen Klopp at Mainz 05 in 2009.
When Klopp left Borussia Dortmund at the end of the 2014-15 campaign, Tuchel also replaced him there, leading the team to German Cup success in 2017.
He joined Paris SG the following year, replacing Unai Emery and winning back-to-back French league titles. Tuchel also took PSG to their first Champions League final in 2020, which they lost to Bayern, before leaving for Chelsea.
Taking over the England national team represents a new challenge for the German, who will be tasked with delivering a first major trophy since England won the World Cup on home soil in 1966.
10°C