Midfielder McEachran, 18, has penned a five-year deal, while full-back Bertrand, 22 next month, agreed a four-year contract.
McEachran 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 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."
He added: "I feel really sorry for Michael (Essien) because he has had a lot of injuries before, but hopefully it will give me a chance to prove myself to Andre (Villas-Boas).
"Hopefully, I will get a run-out against Portsmouth, that would be good.
"I just want to get more minutes this season, if not at Chelsea then I will go out on loan, but I want to play here as much as I can."
McEachran is looking forward to the club's Asian tour, which will feature games against a Malaysia XI and Thailand All Stars before taking on Hong Kong First Division League champions Kitchee and either Aston Villa or Blackburn in the Barclays Asia Trophy.
"It was good to play my first game back against Wycombe this week, good to get some touches of the ball and be back in match situations," he said.
"I went away with the first team last pre-season when we played in Germany for a few days, but this will be the first tour when I go away for two weeks so it should be good."
It remains to be seen whether McEachran, who made 17 appearances for Chelsea under Carlo Ancelotti last season, will be part of the first-team group in the coming campaign, or as he suggested gain some more first-team experience elsewhere.
The academy graduate intends to continue his hard work and progression towards one day becoming a Chelsea regular, having penned a five-year deal.
"A long-term contract is what I wanted since I was a kid, and hopefully I will spend my career at Chelsea," he said.
"It will be good if I do, but 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 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: Team Talk
Source: Team Talk