"I'm just so happy to be joining Arsenal. This is a great club with a world-class manager, high-quality players and a fantastic stadium.
"Everything is set up for Arsenal to be very successful for years to come.
"I have had a good taste of the Champions League during my time with Ajax and this is something I am looking forward to experiencing again with Arsenal.
"I'm also looking forward to playing in the English Premier League, which for me, is the best league in the world. Also, I just want to assure the Arsenal fans that I will give everything for this club and I hope we can enjoy winning some trophies together next season."
The defender won the Dutch league in 2004 but leaves Ajax after a disappointing campaign that saw his side finish third in the Eredivisie and out of the Champions League qualifying places.
Since making his international debut in a 2-0 win away to Luxembourg in March 2006, Vermaelen has made 21 appearances for Belgium.
His signing comes after manager Arsene Wenger admitted in a shareholders meeting in May that his side must shore up their defence if they are to close an 18-point gap between themselves and the top of the league.
"In the passing quality in the final third and in the opposition half, we are as good as Manchester United," he said.
"We have conceded more goals and that is where the difference lies; we have conceded 36, they have conceded 24."
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