The current band - Pete Shelley, Steve Diggle, Chris Remmington and Danny Farrant - will start the shows, before Remmington and Farrant make way for Steve Garvey and John Maher to recreate the group's classic 1978-1979 lineup, Louder Than War reports.
It is suggested that Garvey will then depart the stage and be replaced by founding frontman Howard Devoto.
The band will then play tracks from their era-defining Spiral Scratch EP and songs which later appeared in demo form on Times Up.
It is thought that the shows will take place at the Manchester Apollo on May 25 and London's Brixton Academy on May 26.
Devoto, real name Howard Trafford, and Shelley, real name Peter McNeish, founded Buzzcocks in 1976. Their self-released Spiral Scratch EP is credited with kickstarting the DIY movement in the UK.
The duo played a key role in the early days of punk when they invited Sex Pistols to play two shows at Manchester's Lesser Free Trade Hall in June and July of that year, making their own live debut at the second gig.
Devoto left the band in early 1977 to form Magazine, who themselves reformed in 2009. Shelley became the group's singer and Diggle moved from bass to guitar.
Buzzcocks split in 1981 but reformed in 1989 and have gigged and released new albums since - their reformed incarnation now being active for 17 years longer than their punk-era versions. The band famously supported Nirvana on their final European tour dates in 1994.
In 2002, Shelley and Devoto reunited for the one-off album Buzzkunst under the name ShelleyDevoto.