Demolition of much of the building, which hosted stars such as The Beatles in its heyday, is due to begin in December following the sale of the bulk of the site to investors by Duddingston House Properties.
The buyers, Mountgrange Real Estate Opportunity Fund and PRUPIM, plan to build a 10-storey office and retail block on the site. This backs onto the new Buchanan Galleries extension.
The investors have awarded construction giant Sir Robert McAlpine a design and build contract for the scheme.
The art deco facade of the building on Renfield Street and foyer area will be retained by Edinburgh-based Duddingston House Properties.
The company is thought to be looking for a leisure operator to develop that area. The deal with Mountgrange and PRUPIM appears to sound the death knell for hopes the landmark building may be returned to life as an entertainment venue six years after the last film was shown in the cinema.
In April, theatre impresario Sir Cameron Mackintosh said he may be willing to invest to transform the building into a 2000-seat playhouse on the site.
Sir Cameron said he had commissioned colour sketches of how the playhouse would look.
The plan evoked memories of the days when crowds packed the venue in its guise as the Paramount to see legends of the 1960s music business like the Rolling Stones and Jimi Hendrix. Opened in 1934, the venue became an Odeon cinema but closed in 2006.
Mountgrange Real Estate Opportunity Fund and PRUPIM are set to make a speedy start on creating 143,000 sq ft of Grade A office and retail space on the site. Demolition is expected to be completed by the end of the year. The building is expected to be completed in December 2014.
Nick Berry of Mountgrange Investment Management, which manages the real estate opportunity fund, said: "We have identified Glasgow as a prime target for commercial investment and believe this provides an excellent opportunity to respond to the shortage of Grade A space."
Councillor Gordon Matheson, leader of Glasgow City Council, said: "It is vital to have access to top class office space to continue to attract new businesses and jobs. I am delighted this site is now to be regenerated."
Asked about the potential for traffic disruption, a spokesman for Glasgow City Council said: "Any impact on surrounding roads will depend on the detail of works planned."
In September, The Herald reported Duddingston House Properties, Mountgrange and Prupim were close to a £5m deal covering the bulk of the site.
Sir Robert McAlpine has worked on the Commonwealth Sports Arena and the adjoining Sir Chris Hoy Velodrome in Glasgow. It is constructing a new five-storey building for the Glasgow School of Art which will house studios, teaching facilities and exhibition space.
Duddingston House's plans for an £80m office and leisure development were hit by the economic slowdown.