Mr Moggridge died from cancer at the age of 69.
His computer, the Grid Compass, was designed in 1979 and initially used by the American military.
It retailed at £5,097 ($8,150) and went into space on board the space shuttle Discovery.
The magnesium-cased device was distinctive because the screen display folded down over the keyboard.
Mr Moggridge founded a London-based design company in 1969, which is now a global consultancy firm called Ideo.
He also became visiting professor in interaction design at the Royal College of Art in London and consulting associate professor in design at Stanford University, California.
Mr Moggridge wrote two books, Designing Media and Designing Interactions.
In 2010 he was given a lifetime achievement award by the Duke of Edinburgh.
Mr Moggridge had been director of the Smithsonian Cooper-Hewitt National Design Museum in New York since 2010.
Mr Moggridge is survived by his wife, Karin, and sons, Alex and Erik.