Coetzee has promised to name names when he appears before the five-member committee, but admits the story he intends telling will contain "absolutely nothing new".
Coetzee told Sapa on Monday he was feeling "one hundred percent relaxed" and was confident of receiving amnesty.
During the four-day hearing, Coetzee will testify about his involvement in the murders of prominent Durban civil rights lawyer Griffiths Mxenge and Port Elizabeth law student Sizwe Kondile.
Coetzee has previously admitted to ordering four askaris - turned African National Congress guerillas - to murder Mxenge because he was "a headache" to the security police.
Mxenge was stabbed to death on November 19, 1981 after being abducted and taken to a stadium in Umlazi, near Durban. His throat was slit and his body had more than 40 stab wounds.
Kondile, who disappeared in late 1981, was taken to Komatipoort where he was drugged, shot in the head and burnt on a pyre made of wood and tyres, Coetzee told the Harms Commission investigating police hit squads several years ago.
Coetzee will also tell of his involvement in the abduction of Dyan "Joe" Pillay from Swaziland and his interrogation by police on suspicion of being an ANC regional commander.
Asked whether any new details were likely to emerge in his testimony on these three cases, Coetzee said: "No, absolutely nothing new."
The former police captain, who spent several years in exile after exposing the existence of a hit squad at Vlakplaas in an interview in 1989, will be represented at this week's hearing by Pretoria attorney Julian Knight and advocate Rudolph Jansen.
Jansen said Coetzee would take the stand first on Tuesday to testify about all three murders before fellow amnesty applicants Almond Nofomela and David Tshikilange - two former askaris - were called to give evidence, possibly only later in the week.
Their hearing was brought forward to this week after Natal Attorney-General Tim Mcnally instructed police in mid-July to arrest Coetzee, Nofomela, Tshikilange and former security policemen Brig Johannes van der Hoven and Andy Taylor for their alleged involvement in Mxenge's murder.
The Truth Commission, which has said it believes early amnesty hearings can save unnecessary trials, arranged for the hearing to take place before the trial of the five men resumes on December 2.
Mcnally told Sapa on Monday he had not been invited to attend the amnesty hearing in Durban's Christian Centre and had no plans to send a representative to observe proceedings.
"I am not expecting anything to come out that is new but I will watch developments and react accordingly."
Coetzee, who has previously named Joe Mamasela, Nofomela, Tshikilange and Brian Ngqulunga as Mxenge's killers, told the Harms Commission that Van der Hoven, then commander of the Natal security branch, had ordered him to get rid of Mxenge and make it look like a robbery.
Mamasela is now helping Transvaal Attorney-General Dr Jan D'Oliveira in his probe of third force activities by the police, while Ngqulunga was shot dead shortly after testifying at the Harms Commission.
Nofomela, now serving a prison sentence for the murder of a Brits farmer, was reportedly transferred to Westville Prison near Durban on Sunday in preparation for Tuesday's hearings.
Mxenge's family, which has a R398000 civil action pending against Safety and Security Minister Sydney Mufamadi, indicated on Monday it intended opposing Coetzee's application.
One of Mxenge's brothers, Fumbatha, a Port Elizabeth-based medical doctor, told Sapa the family would argue against the application on the grounds that the murder was not proportional to the political objective being sought.
Dr Mxenge said the family would be represented at the hearings by his brother Mhleli, a director in the Eastern Cape ministry of finance, and his son, Mbasa.