The former Cabinet colleagues were seen “chatting very friendlily” as they drank and ate bread during an interval of Richard Wagner’s Ring Cycle, according to an eyewitness.
Fittingly, the epic music drama is about the struggle for power.
Professor John Hardy, who was also attending the opera in the German town of Bayreuth in Bavaria, said he saw them talking on Wednesday evening, while his wife had spotted them at the previous night’s performance.
He told the Press Association: “They were just chatting friendlily having, I think, a beer or a glass of wine and some German bread.”
Prof Hardy said he was “sure they must have arranged to be there together” and did not seem to be with anyone else.
The four-part opera concludes on Sunday evening, and the University College London neuroscience professor said he expected Mr Gove and Mr Osborne would be there until then.
The opera, which is based on Norse mythology, is said to have taken Wagner around 26 years to complete.
It has been described by Classic FM as the “peak of operatic indulgence, excess and excellence”.
Mr Gove was a key figure in former prime minister David Cameron’s top team, but his decision to back Brexit soured the pair’s friendship.
He was sent to the backbenches when Prime Minister Theresa May came to power in July 2016, but returned as Environment Secretary after the recent General Election.
Mr Osborne, who many saw as positioning himself to succeed Mr Cameron had Remain triumphed in the referendum, was also sacked by Mrs May.
The former chancellor now edits the Evening Standard newspaper and has attacked the PM in a number of scathing editorials and front pages.