City chairman Adam Pearson said: "We have now agreed a transfer fee with Motherwell for Stuart Elliott and also agreed financial terms with the player.
"Stuart is coming to Hull on Thursday to meet with Jan [Molby] and myself when we anticipate concluding the deal.
"To sign a player of Stuart's pedigree would be a major coup for Hull City because he is a player who will make a real impact at our club for a number of years, as he already has done in the Scottish Premier League and on the international stage with the full Northern Ireland team.
"After agreeing personal terms with Stuart we are confident of persuading him that Division Three will only be a stepping stone before returning to a higher standard."
Elliott is set to become City's 2nd highest purchase ever, transferring for just over £200,000. The fee falls just short of that paid for Lawrie Dudfield a year ago.