Private equity group 3i has owned the struggling company since 2007.
Agent Provocateur has 10 stores in the UK and employs around 600 people. It is not known if there will be job losses.
It has been reported that the firm linked to Mr Ashley paid around Â£25m after seeing off competition from private equity firm Lion Capital.
The lingerie firm was sold via a so called "pre-pack deal" - that means a buyer is lined up to buy the assets of a company, but crucially not its liabilities, such as its debt and pension deficit.
It is usually agreed before the company is publicly declared to be in financial difficulty. Defenders of such deals argue that they allow a company to survive and protect jobs.
The deal was done through investment vehicle Four Holdings, which is a third-owned by Sports Direct, according to Companies House filings.
What is a pre-pack administration?
Sports Direct's profits have suffered after criticism of work practices at its Derbyshire warehouse.
Mr Ashley appears keen to target more upmarket fashion retail, moving away from the cheaper end of the High Street.
In February he acquired a 11% stake in fashion chain French Connection, and owns a controlling stake in the premium retailer Flannels, among other interests.
Agent Provocateur was founded in 1994 by Joseph CorrÃ© and his wife Serena Rees.
Mr CorrÃ© is the son of fashion doyenne, Vivienne Westwood and the former manager of the Sex Pistols Malcolm McLaren.
Lingerie firm Agent Provocateur has been bought by a firm linked to Sports Direct owner Mike Ashley after it was placed into administration.