Officers were called at 10.06pm on Monday night to Netpremacy, in Wellington Place, just off Whitehall Road.
Witnesses reported two cars – a blue Ford Focus estate and a black Ford Mondeo estate - had been reversed into the glass-fronted offices before computer equipment, including several laptops and monitors, was stolen.
Both vehicles left the scene along Whitehall Road towards the A643.
A large pane of glass in the office building was smashed in and debris was strewn all over the street.
A tree had been flattened on the grass verge outside the office building and debris was on the pavement outside, including a wheel from a car and glass from the window.
The debris had been cleaned away on Tuesday morning and the window boarded over.
The blue Ford Focus was later found abandoned in Bath Road, Holbeck, and has been recovered for forensic examination.
Netpremacy help businesses with Google Cloud - a method of storing data on the internet. Their clients include Deliveroo, Just Eat and the Government.
Enquiries into the incident are ongoing.
Anyone with any information that could assist the investigation is asked to contact Leeds District CID via 101 quoting crime reference 13190257219 or call the independent charity Crimestoppers anonymously on 0800 555 111.