This claim was made by Vlok in an 84-page amnesty application to the Truth and Reconciliation Commission. Extracts from the application were published in a Cape Town newspaper on Friday.
In the application Vlok alleged that Botha ordered the destruction of Khotso house in June 1988 because it had become "a house of evil" used to store handgrenades, limpet mines and other weapons.
"In this respect his order to me and the SAP was clear: `I have done everything possible to persuade them (the SACC) to come to their senses but nothing helps. We cannot act against the people. You must render that building of theirs unusable... Whatever you do, you must make very sure that nobody is killed'."
Vlok said he conveyed Botha's instructions to then police commissioner General Johan der Merwe, who first confirmed allegations of police involvement in the bombing when he testified at an amnesty hearing last year.
"After the building was so seriously damaged in an explosion that it was indeed rendered unusable... Mr Botha congratulated me and the SAP on the success of the operation during a meeting of the State Security Council."
In his application, Vlok also admitted to falsely implicating African National Congress supporter Shirley Gunn in the bombing in an "incorrectly worded" press statement issued on January 1989.
"...To the extent that it caused her harm, I am sorry and wish to express my sincere regret."
He said he and Van der Merwe also planned the bombing to stop it from being used as a base for guerillas.
Other acts for which he claimed responsibility were the bombings of cinemas showing "Cry Freedom", the Richard Attenborough film about the life of slain black consciousness leader Steve Biko.
"We judged that screening a movie such as "Cry Freedom", with its very clear message of racial hatred, could have sparked further unrest, unhappiness and loss of life."
He said he believed that all operations launched against the "enemy" were bona fide, justifiable and authorised. He accepted that apartheid had resulted in pain and suffering", but Marxism/communism's record was more terrible".