Mascherano, who has been angling for a move away from Anfield, is expected in Spain for a medical this weekend.
Liverpool had rejected two previous Barca bids for Mascherano, and also one from Inter Milan.
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Hodgson was forced to leave him out of the team at Manchester City on Monday when the 26-year-old insisted he was not in the right frame of mind to play.
"There are a lot of factors I don't want to be drawn on too much," Hodgson said in a news conference broadcast by Sky Sports. "But it's not easy to defend his actions because professionals are paid to play and when called upon to do so, they should."
Hodgson had hoped Mascherano would stay on but ultimately the Argentine appears to have got his own way, leaving Liverpool with little time to sign a replacement in the transfer window.
"I don't think players mean it as a challenge to your authority or the club's, but it's a selfish situation where they want to do something and then expect the club and me, in my position as one of the leaders of the club, to bow down and accept they are going to get their way," Hodgson said.
Barcelona said on their website the two clubs had agreed on a transfer that would send Mascherano to the Catalan club for four seasons.
"The deal depends on the utility star passing a medical at Barca and then signing the contract. Mascherano will arrive in Barcelona this weekend," the club said.
Spanish media reported the deal was worth around 22 million euros. Liverpool confirmed on their website a transfer fee had been agreed but did not disclose what it was.
Mascherano would become Barca's third signing of the closed season after the arrivals of Spain striker David Villa and Brazilian full-back Adriano Correia.
He would help fill the gap left by the sale of defensive midfielder Yaya Toure to Manchester City.
Barca are still locked in negotiations with AC Milan to sell Swedish striker Zlatan Ibrahimovic before the end of the transfer window. They begin the defence of their La Liga title away to Racing Santander on Sunday.
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