It was announced on Thursday that Frank was leaving to take charge of Tottenham.
Giles told the Brentford website: “It has been a pleasure working alongside Thomas.
"From the moment he replaced Dean Smith, he understood what we were trying to build and his wisdom, coaching ability and emotional intelligence have helped transform the club.
“There have been so many special moments with Thomas and nobody will ever forget the day at Wembley for the play-off final or that emotional first Premier League game against Arsenal.
“But it’s not just what you see on the pitch. He forged a special connection with our fans, helped develop and improve players, and was instrumental in implementing the culture that has seen Brentford go from strength to strength.
“However, just as when a player leaves, it provides an opportunity for someone else to come in and make their own impact.
“We will never forget Thomas, but now it is time to thank him and take the next steps in our journey with a new leader who we believe can be just as successful and influential.”