The deal becomes effective in July later this year with Puma becoming the official kit supplier of the Premier League leaders.
In addition to producing the playing and training kit for all Arsenal teams, the Germany-based company has acquired wide-ranging licensing rights to develop other Arsenal branded merchandise on a global basis.
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This new commercial partnership represents the biggest deal in Puma and Arsenal's history.
Ivan Gazidis, chief executive at Arsenal, told the club's official website: "We are excited to be partnering with PUMA, a company whose football heritage and record of innovation have a strong affinity with our own.
"This represents another important step forward in Arsenal's progression on and off the pitch."
The north London team last changed manufacturer in 1994, to American-based Nike from previous suppliers Adidas.