Specialist website Vertikal.net said the five axle 110 Tadano Faun ATF110G was owned and operated by Baldwins Crane Hire
It was believed to be lifting a steel beam at around 18:00 hours yesterday, when it overturned.
No-one was injured in the incident which saw the beam apparently land on another beam over an excavation stopping the crane from going over completely.
Tate Modern said: “At approximately 18:00 on 01/12/2011 a mobile crane overturned on the Tate Modern development project in London.
“No injuries were sustained and the crane remained within the site boundary. The crane has been recovered.”