Bougherra told the Scottish Sun: "The gaffer now understands and everything is okay. I told him I'll do whatever I need to do for him. I told him I'll do everything I can to make things perfect.
"I spoke to the gaffer and have 100 per cent respect for him and everything he does.
"It is because of the gaffer I am going to the World Cup finals. He has given me confidence and helped me. I accept anything he does and I want him to be happy with me.
"My objective with Rangers now is to win the three trophies here. Last year we won the double; now we want the treble."
Bougherra claims to have valid reasons for his first two late arrivals from international duty, saying his daughter had a kidney infection on the first occasion - something he insists Smith was aware of - while he had his passport stolen on the second occasion.
This time, he says he missed his flight back to Glasgow after being invited to celebrate Algeria reaching the World Cup with the country's president.
He claims to have sent a text message to Rangers assistant boss Ally McCoist to let him know that was the case but admits he did put his country before his club this time.
"It may be the only time in my life I have such a celebration," he said.
Insisting his head is now "100 per cent on Rangers", he vowed to delay his departure for the African Cup of Nations until until after the Old Firm derby at Celtic Park on January 3.
He said: "I want to play in the Celtic game.
"Now I've come back and I'll do the right thing for Rangers. I know Celtic is a big game and I'll be there."
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