The midfielder produced a fantastic goal in the second half to earn Leicester a historic victory in front of a crowd of 20,000 people -- the largest attendance at a UK football ground since the COVID-19 pandemic began.
The win also sees Brendan Rodgers earn his first ever major trophy in English football.
"It's an amazing feeling, I wasn't aware before I came to Leicester that they'd never won the FA Cup, they'd lost in four finals previous so to be able to give that to the owners and the fans, so special," Rodgers said. "So proud, the board players staff, supporters, an amazing day for the city, so proud for everyone.
A landmark day ended with emotional scenes as Leicester's Thai owner was invited on to the field to celebrate with the team.
Aiyawatt Srivaddhanaprabha's father Vichai, whose ownership helped transform the Midlands club, died in 2018 in a helicopter crash at Leicester's stadium.
"We have a picture [of him] on the inside of our shirts so he's always with us. This is what we've dreamt of and talked about for so long," said Leicester keeper Kasper Schmeichel, whose late saves were crucial to the victory.
The game's first half was slow but was brought to life after 63 minutes when Tielemans scored with a stunning long-range effort.
"It feels really good, it's amazing, I'm really glad to score the goal to help the team to win the game," Tielemans said. "It was a really tight game and to score in the final but what a goal that was. So I'm really happy for the team and for the fans."
The result sees Chelsea lose back-to-back FA Cup finals after suffering defeat at the hands of Arsenal last season.
"We are disappointed and not angry with our performance from the boys," Tuchel said. "I think the performance is enough to win it. I think today we were unlucky and we've never hidden that we need to have that to win at this level.
"You need momentum, decision making, little details, the referee.
Tuchel's side will have another chance to collect silverware when they meet Manchester City in the Champions League final later this month.
It was a very cagey start to the match with the first chance coming after 24 minutes when Mason Mount's strike outside of the area was deflected wide.
Leicester's best chance came when Tielemans produced a lofted pass to Jamie Vardy who headed wide before the break. The first half ended without a single attempt on target from both sides.
Schmeichel made an even better stop with four minutes remaining when he denied a Mount half-volley from inside the box.
Chilwell thought he had grabbed late equaliser but it was ruled out for offside and Leicester held on for the win.
"Youri Tielemans' goal was like an old school FA Cup winning goal but also Kasper Schmeichel's save, those are the special moments you need in games. Overall we were the better team, super aggressive, pressed well, we were always a threat with the ball," Rodgers added.