Henry was still to agree to personal terms on a four-year deal with Barcelona after it agreed to pay Arsenal 16 million pounds (24 million EUR; US$32 million) for the 29-year-old France striker.
"All that remains are to smooth out some details of the operation between the three parties involved in the agreement; that is Arsenal, Barcelona and Thierry Henry," Barcelona said on its Web site.
Henry said he was "honored" to join Barcelona and called his arrival "emotional."
He will undergo a medical on Monday before being presented to the public at Camp Nou.
Henry leaves the English Premier League club as Arsenal's most prolific scorer, with 226 goals in 364 appearances. Henry helped the north London team to two Premier League titles, three FA Cups and the 2006 Champions League final, where it lost to Barcelona.
Though Henry spent much of last season sidelined because of stomach and groin injuries, he remains one of the game's biggest stars with his ability to score quality goals and beat defenses.
Henry led the Premier League in scoring four times and was Europe's top goalscorer twice.
Coming off its first trophy-less campaign for three seasons, Barcelona will field one of the most attacking teams in Europe after clinching Henry's signature.
Henry could line up with two-time FIFA player of the year Ronaldinho, Cameroon striker Samuel Eto'o and Argentina winger Lionel Messi, with all four players combining for 56 league goals this season.
Barcelona is also close to signing Ivory Coast midfielder Yaya Toure.
The Monaco player, brother of Arsenal defender Kolo Toure, arrived in Barcelona on Sunday with an eye to completing his move from the French league in time to be presented as Barcelona's second summer signing after Henry on Monday.