He added: "The Cup final and Wembley Stadium go hand in hand and everybody at the FA is looking forward to a great day."
Wembley Stadium managing director Alex Horne said: "We're delighted with the news and I would like to thank Brent Council for their help during this process.
"We received the keys to the stadium just over a fortnight ago, since then Wembley and the FA's staff have worked incredibly hard to put on two great test events in a very short period of time.
"We realise that there is still some way to go yet and are digesting the feedback we have received in order to ensure that coming to Wembley Stadium is a fantastic experience for fans."
Brent Council chief executive Gareth Daniel said: "We are delighted to be able to hand over this safety certificate, which will allow this 90,000-seat stadium to open, bringing back world-class music and sporting events to Wembley."
The FA also announced that finals of the FA Trophy and the FA Vase will be held at Wembley on 12 and 13 May respectively, at a capped capacity - as part of the build up to the official opening on 19 May.
The keys to the new Wembley Stadium were handed to the FA on 10 March, more than one year after it was originally scheduled to open.
The 2006 Cup final was due to take place there, but had to be postponed after work fell behind schedule.
The ground, designed by leading architect Sir Norman Foster, cost £757m.