The 36-year-old joined Stamford Bridge on a free transfer from Paris Saint-Germain in August, with Lampard keen to add experience to his defence.
Lampard had been in contact with the Brazilian centre-back over the summer to personally put forward Chelsea’s proposal.
Thiago Silva claims Lampard sealed the deal with a picture of them shaking hands as captains before kick-off in England’s friendly against Brazil at the Maracana in June 2013.
And the Brazilian defender says it is a ‘source of pride’ to link up with Lampard at Chelsea.
‘When I was about to sign with Chelsea, when I said ok, he sent me a message with a photo of us shaking hands as captains at the Maracana, in the friendly between Brazil and England,’ said Thiago Silva.
‘It was a big surprise for me, because I didn’t remember that game.
‘I certainly didn’t hesitate to be coached by him. I’m happy that he enjoyed my work so much, I hope to do it in the best possible way to help Chelsea.
‘It is a source of pride to be coached by a player I played against and was one of the greatest midfielders in the world.
‘For me, it is very joyful to share dressing rooms, exchange ideas, and look to help in every way.’
Thiago Silva has impressed since his arrival at Chelsea and has quickly formed a solid partnership alongside Kurt Zouma.
The Brazil international provides a wealth of experience following his time in Italy with AC Milan and his eight-year stint with Paris Saint-Germain in France.
And following his move to the Premier League, Thiago Silva admits he has suffered from headaches following the amount of aerial battles he’s faced.
‘There are three schools in my view that are very different,’ said the Brazilian.
‘I had a great learning experience in Italy, in my opinion important for the defensive phase. I had teachers like [Paolo] Maldini and [Alessandro] Nesta.
‘The last two games I played in England I came out with a headache, aerial duels all the time, constant, very high game pace.
‘So I take a little bit from each school and put it into practice to help the younger players. I am learning in the Premier League, more throughout this year, and hope to learn more.’