"The appointment is permanent," chief executive Peter Kenyon told a news conference on Friday.
Grant, 52, replacing Jose Mourinho who left the club on Thursday, said: "Everything has happened very quickly in the last 48 hours but I am happy to be here.
"I am my own man and I would not have taken the job if I did not think I could do it."
Assistant coach Steve Clarke will continue in his role but Grant will bring in a new backroom staff after Mourinho's four Portuguese colleagues also left on Thursday.
Referring to Mourinho, the self-styled 'special one', Grant said: "I am not a special one, I am a normal person".
Grant, Kenyon and chairman Bruce Buck faced a more gruelling interrogation from the media than is normal on these occasions and the new coach was quick to play down his relationship with Chelsea's billionaire Russian owner Roman Abramovich.
"I did not get the job because I am a friend of Roman Abramovich," he said.
"I have a normal relationship with him. I don't want to talk about being family friends. We have a football relationship."
He also said he did not foresee a problem with Abramovich meddling in team affairs.
"I will take all the decisions in football on my own. He did not try and meddle in the past and will not in the future," said Grant.
Asked what his message was to the fans, many of whom are angry at Mourinho's departure, Grant said: "It touched my heart how they reacted when Jose left and my job is to make them happy.
"But the supporters were here before Jose came and they will be here after I have gone."
NO BUST-UP
Kenyon dismissed suggestions there had been a major bust-up between Mourinho and his players or Mourinho and the board.
"The reality is the last six or nine months have been difficult for everyone (at the club)," he said.
Kenyon added the recent defeat by Aston Villa, last Saturday's home draw with Blackburn Rovers and Tuesday's home draw with Rosenborg Trondheim in the Champions League were not the catalysts for his departure.
"There was no single catalyst. No bust-ups. But we reached the point in the last few days that it was right for him and right for the club to mutually part company," said Kenyon.
He also denied Mourinho was not involved in the purchase of Andriy Shevchenko from AC Milan last year, saying the owner, the board and the manager all agreed on the deal.
Kenyon said Grant was the right man to take Chelsea forward.
"Chelsea is a different club at a different level than it was (when Mourinho took over three years ago)," he said.
"I don't fear an exodus of our star players either. They have all pledged their full support to Avram."
Asked whether Chelsea had taken a backward step in appointing a man with no direct coaching experience outside Israel, Buck said: "We don't believe it's a backward step, we believe it's a step forward".
Buck would not say whether Mourinho's severance package precluded the Portuguese coaching a rival Premier League team.
Grant will not take training on Saturday, the day before Chelsea play Manchester United at Old Trafford, as it is Yom Kippur, the most holy day in the Jewish calendar.
