The Red Devils kept faith in the Norwegian even when they were dumped out of the Champions League earlier this season.
And United harbour hopes of finishing second only to Manchester City, who look likely to run away with the league title, this term.
They have made forward steps in the league having finished 33 points behind champions Liverpool last term despite finishing third in the table.
Tuchel has paid credit to the United hierarchy for sticking to a long-term vision rather than dumping Solskjaer for another manager, with Mauricio Pochettino having been heavily linked with the Old Trafford job before he took over at Paris Saint-Germain, who themselves sacked Tuchel in December.
The German only came in at Chelsea at the end of January, replacing club legend Frank Lampard who paid the price for a torrid run of results.
Tuchel is eight games unbeaten across all competitions since coming in and led Chelsea to an impressive Champions League last 16 first leg win over Atletico Madrid in midweek.
But Chelsea owner Abramovich’s lack of patience with whoever is sat in the Stamford Bridge hotseat has been made clear ever since he took over in 2003.
That was demonstrated again with the sacking of Lampard who had only been in charge for 18 months and is regarded as the club’s greatest ever player by many of their supporters.
Speaking of Solskjaer ahead of Chelsea’s clash with United in west London today, Tuchel said: “We could always feel that even in situations where results were missing, we could always feel from outside that this is the guy, they have found the guy they trust.
“Of course, you wish for it, but in the end you have also to be honest, you have to earn it.
“I assume that this is not a gift for Ole Gunnar Solskjaer that he has this trust.
“I assume he works hard for it and creates on a daily basis an atmosphere everyone is happy with at Manchester United.
“I told you how I felt after this defeat in the Champions League. We all know that defeats are hard to digest.
“Am I a good loser? So so. Maybe not so much, but show me a good loser on this level.
“I would love to turn it around. We love the competition and we love to win and we love a good fight for it, and this is what we will hopefully get on Sunday.”
While Solskjaer said: “Thomas has done really well as it’s never easy coming into a season half way through. But hopefully we can stop that run, that’s my job now.
“We know he has come in and it’s changed a little bit at Chelsea and it’s going to be a great challenge for us.
“But we have improved even though we’re still nowhere near where we want to be – higher up the table and winning trophies.”