He 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.
"It wasn't just wage demands prompting Jimmy to go, but the length of contract too.
"He's 31 this year and we 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 don't think Jimmy owed us anything. I thank him for the year of work he did under me."
Bullard had been the subject of a £5m bid from Bolton last week, but the move failed to go through.
Brown said: "It's shown everyone of how serious, one, Paul Duffen (Hull City chairman), two, Phil Brown and three Hull City is to the Premier League campaign.
"The only way to sell Hull City to Jimmy Bullard is to show him the ambition of the football club, the ambition of the manager and the chairman and play the type of football he likes to play.
"He has been impressed with the way we have approached the Premier League this year and he heard what he wanted to hear."
The former Wigan midfielder was out of contract at Fulham at the end of the 2009/10 season.
The Tigers have also agreed a new contract with left-back Andy Dawson.
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