Alves, a Brazil international, joined Barca from Sevilla in 2008 and has played a key role in a golden period for the Catalan club, winning 19 trophies including three Champions Leagues, five La Liga titles and three King's Cups.
The 32-year-old has made 343 appearances and is one of seven players who won a treble of Europe's elite club competition and the domestic league and Cup in both 2008-09 and again in 2014-15.
"I am really happy," Barca left back Jordi Alba told a news conference at Spain's training base outside Madrid on Tuesday.
"He is a great person and one of the best professionals I have shared a dressing room with," he added. "I didn't really know what he was planning to do but I am really pleased as he is a very important player for us."
One of the most popular members of the squad and a close friend of Argentina forward Lionel Messi, Alves will face stiff competition for his place at right back after Barca signed Aleix Vidal from Sevilla on Sunday.
Spain international Vidal will, however, be unable to play until January as Barca have been banned by FIFA from the transfer market until then over irregularities in the signing of foreign under-18 players.
(Writing by Iain Rogers, editing by Ed Osmond)
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