The 23-year-old signed a five-year deal with the Blues on Wednesday after Chelsea agreed a £50million deal with the Foxes.
Lampard was keen to sign a left-back after failing to settle on a first choice last season, with both Marcos Alonso and Emerson Palmieri failing to impress.
Lampard switched between a back four and a back three last season but Chilwell is adept at left-back and left wing back.
And the England international has revealed that Lampard was the main inspiration behind his decision to join the Blues as the former midfielder won him over with his vision for the club.
‘I am delighted to be joining Chelsea at this very exciting time for the club and the manager played a massive part in me signing here,’ said Chilwell.
‘I think every player wants to play for a huge club in their career and I’m no different, but talking to Frank before I signed really made up my mind that I wanted to come and play here.
‘He installed a lot of confidence in me, he told me about the system he wants to play, how I’d fit into that and he just seemed a really good guy that you could talk to about anything. It’s important to have that relationship and trust with a manager and he’s also very keen on young players being given a chance.
‘We’ve seen that over the past season under Frank, he does play the younger players if they are good enough and just from speaking to him, I’m really excited to be here and I can’t wait to get started.
‘He told me about the system and of course I watched and played against Chelsea over the season, so I know what I’m coming into. I think the way the gaffer sets his teams up is just perfect for me and suits my game perfectly. I’m just can’t wait to get started and hopefully there are many great years to come.’
Thiago Silva is set to join on an initial one-year deal, which will include the option of a further 12 months.
Chelsea also believe they’re closing in on a deal for Bayer Leverkusen attacker Kai Havertz.