The Premier League club confirmed on Sunday (AEDT) that the Dane had penned a fresh contract, meaning he will have spent more than a decade at the Bees should he fulfil his new deal.
Frank arrived at the club in December 2016 as an assistant coach, before being appointed head coach in October 2018, leading Brentford to the Championship play-off final the next season before securing promotion to England's top flight the year after.
Brentford finished its first Premier League campaign in 13th place in 2021-2022, and sat in 10th heading into the mid-season break for the FIFA World Cup.
"Being a head coach at a club is like a relationship; there are highs and lows," Frank said. "I have been here six years in total, which is a long time in modern football, and I'd like to say thank you to the fans for the support you give us – the players, the staff, everyone involved with the club.
"The warmth, support and kindness every time I meet a Bees fan has been amazing and it gives me extra energy to continue the work going forward.
"We attacked the Premier League in the first season and we're attacking it in our second season. I'm looking forward to hopefully continuing our progress and creating more magic moments together."
Having beaten Manchester City 2-1 at Etihad Stadium in its last game before the FIFA World Cup, Brentford hosts Tottenham Hotspur on Boxing Day.