The 47-year-old - who was sacked by Paris Saint-Germain last month - is understood to have been chosen as Frank Lampard's successor after the Chelsea legend was relieved of his duties on Monday morning.
Now, football.london reports that Tuchel has arrived at Chelsea's training complex, and he led his first training session with the players at 6pm.
Most arrivals in the UK are ordered to quarantine for 10 days as part of coronavirus protocols, but Tuchel did not have to self-isolate as he qualifies for an elite sports exemption.
Chelsea are due to take on Wolverhampton Wanderers in the Premier League on Wednesday evening, and the former PSG boss will supposedly be ready to take charge of that game in the capital.
Tuchel is believed to be under orders to propel the Blues back into title contention, as he joins a side who are languishing in ninth in the Premier League table.