Cyclone House, a three-storey office at 17-19 Hardware Lane, sold at auction after bidding from five buyers, following an opening bid of $5.2 million.

The vendors purchased the property for $86,000 in 1970.

"The result has again drawn attention to the market's strong appetite for A-grade investments in Melbourne, both locally and offshore," Allard Shelton director Joseph Walton said.

The property sold with vacant possession after its former tenant, Careers Australia, went into voluntary liquidation in May.

Before it went under, Careers Australia undertook an internal renovation and lavish million-dollar fitout on the building.

The transaction follows another city deal which saw a two-storey shop at 268 Russell Street sell for $3.5 million.

The price reflected a rate of $21,875 a square metre on the building's gross leasing area, Ross Mercorillo, managing director of CRS Property, said.

"This is a record for this pocket of the Melbourne CBD," he said.

"Key CBD locations with upside are highly sought after and investors are prepared to look at the long-term benefits of these assets," Mr Mercorillo said.

The property was leased to Elite Real Estate agents.