The two clubs agreed a £2.5m fee for the 23-year-old Guinea international earlier in the season and the player has now accepted personal terms, while manager Phil Brown has revealed he is in talks with Bullard.
''Hopefully in the next 24 hours we will have another new player in Jimmy Bullard'', he said. ''It is an ambitious attempt but it is a sign of how serious [chairman] Paul Duffen is, how serious Phil Brown is and how serious Hull City is with regards to this Premier League campaign.''
Fulham boss Roy Hodgson confirmed that Bullard's negotiations over a new contract at Craven Cottage broke down over his wage demands and he is about to lose the midfielder for a fee believed to be £5m.
Hodgson said: ''It's disappointing to lose Jimmy. We said all along that we'd like to keep all of our players but the possibility of Jimmy leaving has been there all the time.
''He's been seeking the type of contract we couldn't give him. I congratulate Hull and Jimmy on getting the contract he wanted. There's still some paperwork to be completed. But my understanding is Jimmy has agreed a contract which just needs finalising.
''It wasn't just wage demands prompting Jimmy to go, but the length of contract too. He's 31 this year and didn't feel able to provide him with the contract he wanted.
''The transfer fee that has been negotiated is suitable for a player of his age. I thank Jimmy for the year of work he did under me.''
The Jamaica striker returned to parent club Wigan this week after a dispute with Brown over team selection and has since been loaned to Middlesbrough.
The fall-out occurred after King took exception to Brown's decision to leave him out of the starting line-up for last week's clash against Arsenal.
Brown said: ''We had an agreement with Wigan in case there was any interest in Marlon in the January transfer window.
''If that was at Hull he could stay until the end of the season and make it a permanent deal. If it was elsewhere Wigan, ourselves and whoever could exercise the right for Marlon to move.
''There has been a well documented fall-out, although it was more of a disagreement about team selection. At the end of the day it is my decision. He can voice his opinion in private, one to one, but in front of the players it is a bit different. 'For me it was time to part our ways.''