The Japanese striker has become the club's second signing of the summer transfer window.
The Gunners confirmed a move for the Sanfrecce Hirsohima forward on Sunday, with the player set to complete his transfer when he passes a medical and is granted a work permit.
He becomes their second signing of the summer after they secured a deal for Borussia Monchengladbach midfielder Granit Xhaka before the start Euro 2016.
While the Swiss midfielder is likely to be a first-team regular next season, Asano is one that has been secured for the future. And Wenger says he is looking forward to watching him develop over the next couple of years.
“Takuma is a talented young striker and very much one for the future,” he told arsenal.com.
“He has had an impressive start to his career in Japan and we look forward to him developing over the next couple of years.”
Arsenal fans will be hoping that Asano is not the only striker to arrive at the Emirates this summer.
They are keen to see a world-class centre forward added to the squad for next season after Olivier Giroud and Theo Walcott struggled for consistency last season.
They have already seen Leicester City star Jamie Vardy turn down a move to the club but will be hoping that Wenger has another move planned instead to avoid more disappointment in the campaign ahead.