Both the YP and its sister title the Yorkshire Evening Post are to be printed at JP’s centres at Dinnington, near Sheffield, and Sunderland.
Johnston Press has confirmed that 25 jobs are under threat as a result of the closure.
The Yorkshire Post has been printed in Leeds continuously since 1754.
Pete Lazenby, from the National Union of Journalists, said: “This is an end of an era of importance not just to the newspaper and the newspaper industry but to Leeds as a city.
“It’s an event of historical importance and we shouldn’t allow this to pass without having some form of commemorative event to mark the occasion. It’s a tremendously sad moment.”
Stephen Hart, regional officer for Unite, which represents print workers, said: “It’s not a surprise really, we have had round after round of redundancies within the print facility. We expected the final axe to fall.”
He said staff may be offered roles at the Dinnington or Sunderland plants but he did not expect many to make the move.
The company’s chief operating officer Danny Cammiade said in a statement: “Consultation has begun on a proposal to close the press plant at Yorkshire Post Newspapers in Leeds. If the proposal goes ahead it could affect up to 25 jobs.
“Printing of the Yorkshire Post and Yorkshire Evening Post would move to other Johnston Press plants at Dinnington, near Sheffield, and Sunderland.
“New printing arrangements would allow additional colour in the two newspapers and follow the pattern across the newspaper industry of printing being centralised into fewer but bigger and more modern plants.
“The Wellington Street building would remain a base for nearly 500 editorial, commercial and support staff. Any changes to printing would take effect in March following a full and proper consultation process.”