"This course will be continued, there's no doubt about that," Sobotka told a press conference in Vienna. The 60-year-old, who is a newcomer to national politics, said he did not want "any experiments".
The pair will swap jobs later this month as part of a reshuffle within the conservative ÖVP party announced on Sunday evening.
Mikl-Leitner is set to take over Sobotka's current position as acting regional governor in her home state of Lower Austria.
"In a few days I will leave the republic's toughest job behind me and start the most beautiful role in Austria," Mikl-Leitner said.
The 52-year-old, who took office in 2011, has been one of the key architects behind the country's tough asylum-seeker policies, as Europe grapples with its worst migration crisis since World War II.
She has overseen the introduction of border fences, tougher frontier controls and hardline asylum rules - including an annual cap on migrant numbers - as part of her push to build "fortress Europe" and shut the main Balkan migrant trail for good.
With that route now closed, Mikl-Leitner recently turned her attention to the Italian border, threatening to clamp down on the strategically important Brenner pass checkpoint if Rome failed to stop illegal migrants.