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Park, 26, who was a former target for Premier League rivals Fulham, will cost the Gunners between £3m and £5m.
Arsenal manager Arsene Wenger said: "He will add true quality to our attacking forces and will be a valuable addition to the squad."
The South Korea captain had been close to signing for French side Lille until Arsenal's late bid.
The deal for the former Asian Young Footballer of the Year is subject to the completion of formal registration processes.
Park, who is set to wear the number 9 shirt, said: "I am very honoured and I feel very happy to be at Arsenal.
"It is a dream to be here and I am really proud to be an Arsenal player.
"Now I just want to show how good I am and prove myself.
"In my opinion this is a great club, now I have to show what I can do on the pitch.
"I will do my best, I will never give up, I will show heart, I will give everything and I hope [the fans] will support me."
Lille were surprised at events on Saturday, claiming Park had failed to show up for the second part of his medical after agreeing terms to join the French champions.
Park had been due at the northern French side to continue with the pre-signing examination, which he had begun on Friday, Lille said.
"From what we understand he could be at Arsenal. Everything had been agreed." said Lille president Michel Seydoux.
"We haven't had a telephone call, nothing. Lille are baffled."
In the 2010 World Cup, Park scored an own goal in a 4-1 defeat by Argentina. In South Korea's next match he scored a crucial free-kick in their 2-2 draw with Nigeria, which helped South Korea through to the last 16 of the tournament.
Arsenal have reached an agreement to sign South Korea striker Chu Young Park from Monaco.