Defenders Chilwell, Silva and Malang Sarr all committed their futures to the west London club this week with Lampard heavily reinforcing his back line.
They join Hakim Ziyech, Timo Werner and former Barcelona youngster Xavier Mbuyamba, who have already been signed in this transfer window.
Chelsea’s business looks unlikely to end there, with a club-record £90million fee reportedly agreed with Bayer Leverkusen for their talented midfielder Kai Havertz.
Chilwell comes in after an impressive season for Leicester City in which Brendan Rodgers’ side narrowly missed out on a top-four spot.
Lampard has high hopes for the 23-year-old England international, who cost the Blues around £50million to prize away from the Foxes.
‘With Ben Chilwell, he is a player I know very well, he has been pretty much England’s first-choice left-back now in recent times,’ Lampard told the club’s official website.
‘Great qualities in terms of how he can join in, he is athletic, his physicality, the way he plays and the quality of his left foot, so for us in terms of how he can help out on the left side, attack-wise and defensively, which of course is always first and foremost.
‘I am excited to work with him so I think he is a great addition. At 23 years of age, it is a really positive one for us.’
Thiago Silva, meanwhile, moved to Stamford Bridge on a free transfer after eight years at Paris Saint-Germain.
The veteran Brazilian – who turns 36 next month – won seven league titles in France, while his side narrowly lost out to Bayern Munich in the Champions League final last week.
Lampard is expecting the former PSG captain to add plenty of experience to Chelsea’s defence.
‘With Thiago Silva, we are looking at a player I know very well, pretty much as we all do,’ the English boss added.
‘We have a relatively young squad, we saw that last year, there were games afterwards when I was probably asking for more voice and some more leadership in different ways and he brings that naturally straight away, and also on the pitch he can help talk and be the player that he is which means affecting others.
‘On those levels I hope he brings that. I am pretty sure he will with the qualities we know he has, so I am excited for when he joins up.’