The champions of Europe completed the signing of the 28-year-old on Thursday on a five-year deal.
Lukaku is now the record signing at Stamford Bridge after the Blues defrayed a mammoth £97.5 million.
"We're very happy to have Romelu back in our squad. In terms of personality, speed, power, he can hopefully be an excellent addition for us,” Tuchel said in a press conference ahead of Chelsea’s Premier League opener against London rivals Crystal Palace.
"He has the power, he has the physique to help us. He has the experience and personality to have a huge impact. At the same time, he's a humble guy and a true team player. He cares about Chelsea, so we all decided it was worth trying and fighting hard - and we're happy that he's our player now.
"He was super hungry to come back to Chelsea, he did everything he could to make it happen. He had a huge impact at Inter Milan, he was a huge player with all the responsibility on his shoulders and a big title for Inter last season, so it was actually very important to us that it was his desire to re-join Chelsea and to finish his story and his project at Chelsea in the way that he wants."
Lukaku first joined as an 18-year-old in 2011 but could not break into the first team despite series of loan spells at other Premier League clubs.
He joined Everton on a permanent deal in the summer of 2014 before joining Manchester United and eventually Inter Milan.
He arrives at Stamford Bridge as a complete striker now, having guided the Nerazzurri to their first Scudetto in eleven years.
He scored 64 goals and provided 16 assists in 95 games during his time in Italy.
