Sroubek was jailed in 2016 for five years and nine months after being convicted of importing 5kg of MDMA with a street value of $375,000.
The conviction came four years after a judge discharged him without conviction despite being found guilty of having a false passport and lying to immigration officials.
Sroubek, who was declined parole last month, would have been liable for deportation at the end of his prison term.
Lees-Galloway said Sroubek was granted residence subject to significant conditions.
"The decision to grant residence was made after careful consideration of all the information available at the time. For privacy and legal reasons, I am unable to disclose this information or comment on specific details of the case. It's not a decision I've taken lightly," he said in a statement.
Decisions by the Minister of Immigration to cancel deportation liability and grant residence are made at his "absolute discretion". Legally, this means such decisions can't be applied for, the minister is not obliged to consider any request, nor is the minister required to provide any reasons for any decision made.
Absolute discretion decisions are often the last option available for people to remain in New Zealand for cases outside ordinary immigration settings.
Woodhouse said he had made similar decisions when he was the minister but had explained them publicly.
Sroubek came to New Zealand from the Czech Republic in September 2003 to start a new life as Jan Antolik after fleeing corrupt police who wanted him to lie and clear the main suspect in a murder investigation.
Instead, he left a videotaped witness statement which was later crucial in convicting the killer.
He fled the Czech Republic with a doctored passport but was unmasked in October 2009 when Czech police gave New Zealand police details of his identity and an arrest warrant on minor charges in connection with the 2003 murder.
Sroubek pleaded not guilty to the charges but admitted using a false identity to come to New Zealand.
His defence was he had a "reasonable excuse'' to give a false name as he had fled his homeland in fear of corrupt police officers and a criminal.
The Crown did not dispute his story but said Sroubek should have revealed his true identity to New Zealand authorities.
A jury convicted him in 2011 but Judge Roy Wade gave him a second chance, as a conviction would provide grounds for automatic deportation for the representative kickboxer.
He believed Sroubek would still be in danger from corrupt Czech authorities and the man he helped convict of murder if he were deported.
Four years later, Sroubek was convicted on the MDMA charge. He appealed against that conviction last year, saying the MDMA was planted to frame him.
Revenge, by the person he helped convict of murder in the Czech Republic, was the motive given for the alleged framing.
The Court of Appeal rejected his appeal.
Sroubek has had other brushes with the law in New Zealand.
He was arrested in Operation Ark, a drug investigation, just days after his false passport trial in 2011.
He was later convicted of being a party to the manufacture of Class C drugs, although the conviction was later overturned on a technical ground.
Sroubek was also previously acquitted of committing an aggravated robbery with two members of the Hells Angels.
