The sculpture was based on an 18th century watercolour of the mathematician and scientist Isaac Newton by the artist William Blake.
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However the work, which dates back to 1989, actually depicts the artist, who had a long fascination with robots.
It has now been installed outside the main entrance to the Scottish National Gallery overlooking East Princes Street Gardens.
Paolozzi’s work will also be facing east towards Leith, where the artist, the eldest son of Italian immigrants was born in 1924.
A crane and a gimble were used to get the sculpture into the right position after a two-day operation to relocate the work, which weighs around a tonne.
The National Galleries of Scotland said “extensive pre-planning” went into the relocation of the sculpture, involving curators, conservators, collections management staff and specialist movers.
Paolozzi, who died in 2005, donated many of his works and material from his archives to the National Galleries in 1994. The studio of the artist has been meticulously recreated at the “modern two” national gallery, where the Master of the Universe sculpture was previously on display.
Dr Patricia Allerston, deputy director and chief curator of European & Scottish art at the National Galleries, said: ‘We wanted to bring the art outdoors and into the gardens at the National to spotlight that we are a gallery from the moment people arrive in the gardens.
“We wanted it to welcome people in and to show a snapshot of the incredible Scottish art on offer inside.
“Paolozzi seemed like a perfect choice for this spot, he was very much an artist who looked to the past as well as to the future, which is very much what we are about at the National Galleries.
“He was also from Edinburgh, which seemed very fitting as he will now be looking out over the city and facing towards his hometown of Leith.”
The National Galleries acquired the Master of the Universe sculpture from Paolozzi in 1990, the year after it was made. A larger version can be found in the courtyard of the British Library in London.
A spokesperson for the National Galleries said: “Paolozzi used the same pose as in the Blake drawing but has mechanised the figure.
“The artist also fashioned it to put himself in the picture, creating himself as the sculpture.
“Interested in the relationship between nature, science and the man made, Paolozzi brought all of this together to create Master of the Universe.
“While this statue highlights his ongoing interest in the art and intellectual ideas of the past, which is why we have moved it, the interface between popular culture and technology was a central preoccupation of his art.
“During the late 1940s he made Dada-inspired collages combining magazine advertisements, cartoons and machine parts, thus anticipating Pop Art. Paolozzi produced comparatively few sculptures until 1956 when he invented an unusual assemblage technique which parallels the collage process.
“He pressed objects such as cogs, nuts and machine parts into clay to leave an imprint, poured wax over the surface, lifted the wax off when dry, and constructed sculptures from these wax sheets. The fragile assemblage would then be cast in bronze.
“The shattered, encrusted figures that emerged seem like survivors of a nuclear event, at once noble, menacing and fragile.”
