McEachran, 18, has penned a five-year deal, while full-back Bertrand, 22 next month, agreed a four-year contract. The midfielder was part of the Blues' FA Youth Cup winning side in 2010, and has made 17 first-team appearances, including four starts.
Bertrand joined Chelsea from Gillingham in July 2005 and had productive loan spells in the npower Championship with Norwich, Reading and Nottingham Forest, returning to make his Chelsea debut as a substitute against Birmingham in April.
McEachran intends to work hard as he looks to continue to progress, telling the club's official website: "I need to keep working. This season my target is just to play more minutes.
"Hopefully I will play more games and keep improving."
Bertrand is in no doubt Chelsea provide a bright future under new manager Andre Villas-Boas.
He said: "It is a big commitment, I see the club going in the right direction. I want to stay here, it's the reason I came here six years ago and it's refreshing to have the new manager come in.
"I am looking forward to listening and learning from him. I can see the manager is young and hungry and wants to take the club forward so I want to be part of that and I thought it was best for me to stay.
"Obviously Ashley [Cole] is number one left-back but hopefully I can get a game here and there.
"I am aiming to get a few more games. I hope to stay here this season and hopefully catch the manager's eye."
Source: PA
Source: PA