Dr Hoffman, who was on a cruise ship which stopped at Douglas, was entertained by the ManSat Group, a Manx-owned private company which specialises in commercial space activities.
A whistle-stop tour of the island included the visit to the Foxdale Observatory, where Dr Hoffman met members of the Isle of Man Astronomical Society.
A professor of aeronautics and astronautics at Massachusetts Institute of Technology (MIT), Dr Hoffman made five space flights over an 11-year period between 1985 and 1996.
He was also part of the first mission to repair the Hubble Space Telescope in 1993.
Mike Newby, chairman of the Isle of Man Astronomical Society, said: ‘It was great to be able to welcome such an accomplished yet modest astronaut to our Observatory.
‘Jeff was able to convey to us the excitement of space travel and the wonder of viewing the stars from space, in a way that we could all relate to.’
Dr Hoffman commented: ‘I was impressed with the observatory and I wish that I could have stayed until nightfall to enjoy the beautiful dark skies in that remote corner of the Isle of Man.
‘It’s really impressive how ManSat, a small company on a small island, has made a large impact on global telecommunications.
‘I look forward to a return visit.’