Everton rejected an opening offer of £3.5m from Liverpool a week ago, but Gerard Houllier has now returned with a bid that gives the Goodison club a small profit on the £5.75m they paid Middlesbrough in 1996.
England Euro 2000 squad member Barmby will complete his controversial move to Anfield when he returns from holiday.
Barmby stunned Everton recently by rejecting a £27,000-a-week contract that would have made him the highest paid player in the club's history.
And boss Walter Smith then revealed Barmby had snubbed the deal because he wanted to play for Liverpool.
Everton rejected an opening offer of £3.5m from Liverpool a week ago, but Gerard Houllier has now returned with a bid that gives the Goodison club a small profit on the £5.75m they paid Middlesbrough in 1996.
Everton said in a club statement: "Everton and Liverpool have today agreed the transfer of Nick Barmby to Liverpool in a package worth up to £6m.
"The clubs wish to emphasise that negotiations have continued over the past week in a spirit of goodwill and integrity, and they both wish each other success in the forthcoming season."
Liverpool boss Houllier is an avid Barmby admirer, and stepped up his interest after the player returned to the international stage with outstanding performances for England against the Ukraine and Malta.
And after signing Barmby, Liverpool will then move to snap up Middlesbrough's £5m German international Christian Ziege.