The rockers will perform their new single, No.1 Boy, on the famous BBC music show – exactly 30 years after they first appeared on the programme.
The original band has reformed after a break of three decades, and the punk five-piece have been heartened by their fans’ reaction.
An eight-date British tour is well on the way to a sell-out and a brand new single will be released on January 2.
And guitarist Jo Callis has admitted the band are “incredibly excited” about being back in the spotlight.
Fronted by female vocalists Eugene Reynolds and Fay Fife, The Rezillos best known chart hit was their song Top of the Pops which reached the Top 20 in 1978.
The cartoon punks first formed in 1976 after meeting at art school in Edinburgh.
After the initial split in 1978, vocalists Fay Fife and Eugene Reynolds went on to form The Revillos – a side project that lasted considerably longer than the original band did.
Callis also went on to enjoy huge success after joining chart-toppers the Human League.
He said: “It’s been a long time coming but The Rezillos are finally back.
“There is so much tosh in the charts just now that it just feels like the right time to get back together.
“We weren’t sure about the reaction to re-forming but the ticket sales tell you there are an awful lot of people still wanting to see the band.
“We are all incredibly excited about the public’s response, and just can’t wait to get out there and entertain people.
“After all, that’s what this band are all about – having fun.
“It’s going to be great having our new video on Top of the Pops. A bit like The Rezillos, the programme is a British institution and it seems apt that we are to be brought back together after all these years.”
And the tour was deemed such a success The Rezillos decided to play a larger US tour, then wowed fans in Europe with some incendiary performances.
This weekend The Rezillos play gigs in Aberdeen, Glasgow and Edinburgh, and their new single No. 1 Boy is on general release from January 2.