Tuchel was pleased to see his team take a huge win in the top-four race against Leicester in front of returning fans at Stamford Bridge.
Antonio Rudiger gave Chelsea the lead after restart before Jorginho extended the lead through a penalty, Kelechi Iheanacho pulled one back for Leicester.
The former Manchester United captain's induction follows those of strikers Eric Cantona, Alan Shearer and Thierry Henry.
Manchester United have lost their last two matches in the Premier League against Liverpool and Leicester City.
About 10,000 supporters will return to Old Trafford for the first time in 14 months when they play Fulham on Tuesday.
Eric Cantona is the latest player to be inducted into Premier League Hall of Fame, joining Thierry Henry and Alan Shearer.
On this day in 2019, Manchester City won the FA Cup - and entered the history books as England's first domestic treble winners.
A number of notable former England footballers, including Gary Neville and Gary Linekar, launched a campaign to bring an independent regulator for the sport.
After Liverpool's Alisson Becker scored the winner against West Brom, we look at the five goalkeepers who scored PL goals before him.
Alisson Becker became the sixth goalkeeper in Premier League history to score a goal and the first goalkeeper to score for Liverpool in the club's history.