Henry, who returned from the World Cup last week after France's surprise early exit, agreed a move before heading out to South Africa following a season when he has spent most of the time on the bench.
"Now it is up to him to complete it," Barca director Joan Oliver said on the club website after the last board meeting under outgoing president Joan Laporta.
"This will allow Barca to save money on his wages in the next financial year."
Henry, 32, was reputedly one of the highest paid players in Pep Guardiola's squad and had one year left on his contract.
He has been linked with a move to the New York Red Bulls in the United States.
Barcelona have also been negotiating with Manchester City over the future of Toure who, like Henry, had requested a transfer.
"The decision is in the hands of the player and his representative," Oliver said.
"All that needs to be agreed is the player's terms with the new club."
Toure, 27, lost out to Spain midfielder Sergio Busquets in the battle for places in Barca's midfield last season and has been seeking a move to gain more regular first-team football.
Ivory Coast were knocked out of the World Cup in the group stage.
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