Henderson has signed a two-year deal with the Bees after being granted a free transfer by Ajax.
Brentford manager Keith Andrews welcomed the midfielder's arrival, stating: “When we became aware of Jordan’s availability, it was a pretty simple decision.
“We did our due diligence around his recent games to see where he is: he’s still phenomenally fit and he’s still phenomenally motivated to achieve things in the game, having already achieved a lot.
“With the void of experienced players leaving the building - Christian Nørgaard, Mark Flekken and Ben Mee - it was important to replace that.
“We’ve got a pretty young squad, overall, and we’ve got a lot of club experience, which is really important, with the likes of Vitaly Janelt, Mathias Jensen, Ethan Pinnock and Josh Dasilva, who is still at the club doing rehab.
“But what Jordan will bring is that he has been one of the most influential leaders in modern Premier League years. He’s been at the forefront of driving for titles and Champions Leagues at a fantastic football club.
“He also has experience at international level with England and, with that, comes a level of experience, professionalism and dedication to his profession - that’s the exact way we want to be as a football club.
“He will drive standards and be a brilliant addition to the squad.”
Always admired Brentford
Meanwhile, Henderson explained his decision to commit to the Bees.
He said, “I’m delighted that I’m here; I’m very excited to get started and get going.
“I’ve always had huge admiration for the club and what they’ve achieved over the last few years, in particular, how they’ve grown as a club.
“I’ve been told how organised and well-run the club is, it’s very family-oriented, which I think is very important.
“When I spoke to Phil Giles, Lee Dykes and Keith, I just had a really good feeling about everything. As soon as I had that conversation, it was clear for me that I wanted to come here and it was an easy decision in the end.
“When I spoke to Keith a few times, he was very good and very honest, and he’s excited to get started as well.
“He was another big reason why I wanted to come and try to help the club keep moving forward.”