Mark Devlin, who worked extensively with the 65-year-old at the League One outfit, says he is "delighted" that the former Manchester United director has been appointed
The decision, which is subject to FA Council, will see the former Manchester United director leave his current role with the Bees at the end of the season.
And Devlin, who has worked with Dyke during his time as non-executive chairman of the League One side, says he is delighted for the man who has worked with the club since 2006.
"I'm personally delighted for Greg. He's a man who knows football both through his time working at Manchester United and obviously in his role at Brentford.
"He's got an opinion on everything and he's not frightened to give that opinion. I think if you're trying to achieve something and drive things forward then you need people who are opinionated.
"I think the FA have chosen wisely and everyone at Brentford wishes him all the best and thanks him for everything that he's done during his six, getting on for seven, years at the club."
The Bees are currently just two points off top spot in League One, and Devlin says Dyke will leave the club in "good health" after a tumultuous period at Valley Parade.
"I think, with his background, he's helped to raise the profile of the club," he added.
"The club has enjoyed more column inches and a better profile than maybe it would have done otherwise. Certainly Greg's background and his contacts and his gravitas generally have helped us move the club forward.
"I think at one point Greg even dipped his hand into his pocket and put money into the club when the club needed money a few years ago when it was on its knees.
"He will be leaving a club that's ambitious and will hopefully be playing its football in the Championship, everyone at the club hopes, with a new stadium in the offing. Greg has played a big part in that as well, and the aspirations that the owner has got are firmly on track. So he leaves the club in good health and he's helped the club through some turbulent times."