Thiago made his switch from Bayern Munich to Anfield on Friday having been linked with move throughout the summer transfer window.
The deal was done in time for Thiago to be able to make his Reds debut today with the Premier League champions travelling to Chelsea.
Thiago was part of the Bayern team that dumped Lampard’s Blues out of the Champions League last season.
And the Chelsea boss has acknowledged the quality of the player arriving at Anfield, saying before the move was completed: “Thiago is an incredible player.
“As you say we saw him first-hand - quality on the pitch, personality on the pitch and off the pitch.
“The quotes from [Bayern Munich boss] Hansi Flick this week have been talking about him on both fronts and when you hear that from their manager, who has just such success with him at the centre of the team, I think it speaks for itself.
“He is an absolute world-class midfielder in the modern day. If he does come to the Premier League it will be a big plus and a big plus for the team that he comes to.”
Thiago can’t wait to get going for Liverpool with the former Barcelona ace set to wear No 6 for his new team.
He said: “I am excited not just to wait to play here, but also to train with my teammates, to get to know the coach and what he wants, how the team plays.
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“I want to help the guys if I can help them to be even better than they are, and I can be better than I am. It would be so nice and I hope for that.
“I think in all teams in the world we must deserve to play – that’s what we are training for.
“Also, we have to know to enjoy when you are playing, but also when you are on the bench to help your teammates. I am there for everything.”