He will also accept that other officers, who are not racially motivated, are perceived to be racist by members of the public. He will deny, however, that the force suffers from institutional racism.
Sir Paul will also announce a new training programme to counter racism in the force when he reads from a previously submitted report.
In the 10-page report submitted in July, he says: "We recognise that, in the eyes of individuals and communities in London, police action may be perceived and experienced as racist, regardless of the intent behind the actions.
"On some occasions the racist behaviour may be intentional on the part of the police officers. On other occasions, even though the racism may be unintentional, it is experienced as racism by the member of the public. Both forms of racism are wrong and must be prevented."
His admission is his clearest yet of the problem of racism within Britain's largest police force. He has previously apologised to Stephen Lawrence's parents for the failure of his officers to investigate their son's murder properly, but denied that racism was a factor.
The report focuses on three main themes: the investigation of racially motivated crime, the prevention of such crime and the development of a non-racist police force. Sir Paul will outline plans to improve investigation of racially motivated crime.
"Through openness and partnership we must demonstrate to the people of London the sincerity of our ambition to build an anti-racist police service," he states in the report.
A Metropolitan Police spokesman said yesterday: "Sir Paul does not accept that the force is institutionally racist. He accepts, though, that improvements can be made.
"One example is the assumption an officer might make about a person's body language. The officer might think the body language suggests a person is acting suspiciously when in reality the body language may be cultural."
Sir Paul's appearance before the inquiry in London comes a week after its chairman, Sir William Macpherson of Cluny, said he felt that racism was endemic within the police service.
There have been many demands for Sir Paul to appear before the inquiry, currently hearing from groups not linked directly to the murder of Stephen Lawrence by a white gang in 1993. Some, however, will see it as another rearguard action to defend not only his own position but the sorely- damaged reputation of the Met.
Assistant Commissioner Denis O'Connor and Deputy Assistant Commissioner John Grieve, director of the Racial and Violent Crime Taskforce, will also appear on Thursday.