David Letterman has expressed, on the air, that the Foo Fighters are his favorite band, so it's no surprise that they will be preforming on the final "Late Night" episode on Thursday.
It is one of the only details known about the show's finale, which was taped this afternoon and airs tonight. According to CNN, there will be some "surprise appearances" and a final farewell from Letterman that is not scripted. Notably, Jay Leno, who Letterman went head-to-head against in the world of late night television for years, is rumored to not be in attendance.
Dave Grohl and company famously were the first musical guests to perform for Letterman after the host returned to "Late Night" following his quintuple bypass surgery in 2000. For that appearence, one of the band's many, the Foo Fighters played their hit song "Everlong." Introducing the band that night, Letterman said "My favorite band playing my favorite song..."
Five years prior to that performance, Letterman hosted the Foo Fighters for their television debut. The band played the lead single off their self-titled debut, "This Is A Call."
In the past few years, Letterman's favorite band had a week-long residency at the Ed Sullivan Theater and performed a full concert at the venue leading up to an appearence on "Late Night". It's anyone's guess as to which song (or songs) the Foo Fighters will play to send off Letterman, but expect the host to express how much the band means to him, like he most recently did in 2014 before their performance of "Miracle."