The teenager announced he would be moving to Stamford Bridge this summer earlier in the week but after passing a medical, the Premier League champions have concluded the formalities surrounding the deal.
The Blues have long been linked with Nathan, who earlier this week revealed he was set to join Chelsea after confirming the move on his Instagram page.
Nathan made his first-team debut for Atletico Paranaense in May 2014 and??has represented Brazil at Under-17 and Under-20 level.
A statement on the club’s website said: “Chelsea Football Club is delighted to announce we have agreed terms with Atletico Paranaense for the transfer of Nathan.
“The 19-year-old Brazilian will join us on 1 July. Nathan, who has passed a medical and agreed personal terms, has earned a reputation as an attacking midfielder with an eye for goal and impressive pace.
“Nathan, full name Nathan Allan de Souza,??has represented Brazil at Under-17 and Under-20 level. He scored five goals in five games at the Under-17 World Cup in 2013.”
Nathan added: “I am very happy to be joining Chelsea, the champions of England, and I hope I will be able to learn a lot and develop my game.”
Nathan is the latest in a long line of Brazilian-born players to have been signed by Chelsea, with Filipe Luis, Ramires, Willian, Diego Costa, Oscar, Lucas Piazon and Wallace also on the books at Stamford Bridge.