Flowers has agreed to link up with the Premier League side alongside Steve Wigley as assistant to new boss Iain Dowie following his appointment as manager of the Tigers on Wednesday.
Flowers had been with the Cobblers since February, with Sampson wishing the former Blackburn and Southampton stopper well following his decision to move on.
"Tim goes with our best wishes and this is a fantastic opportunity for him to work at a Premier League club," said Sampson.
"He might only have been with us for a few weeks, but he has been a big help to us and while we know this is a great move for him, we're sorry to see him go.
"Being both a friend of Tim's and a Hull fan as a boy I hope he can help Iain Dowie keep Hull in the Premier League and we wish them well. We will look at bringing a replacement in for Tim and make an announcement in due course."
Source: Team Talk
Source: Team Talk