In the end, what made Meursault realise/accept that he will be executed?

There is a heavy overdose of existentialism here. Meursault is a tortured soul trying to find happiness in a world that would go on with or without him. His death is inevitable, everybody's death is inevitable. While in prison he realizes that just as he “lived (his) life one way, (he) could just as well have lived it another…nothing would matter". In the end we all return to dust. Meusault is content to let this be his time.