The new site on Avonmouth Estate will store 1,800 tonnes, and was operational as of 20 June 2011.
The company's delivery fleet has also been increased to allow for an extra three runs from the Bristol location.
Nina Wilde, Bristol branch manager, said the new site had already had huge interest from the local print community.
She said: "In tough times, it is fantastic to see EBB invest in this area and my team.
"Our new facility will allow us to have a broader range of products and deeper stock range so that we can maintain service levels to customers large and small."
EBB is looking to expand further into the Bristol, Gloucester and South Wales areas, according to sales and marketing director Chris Sandwell.
He said: "This new facility will give us stock on the spot so that we can be both efficient and competitive."
EBB now stocks 18,000 tonnes across 10 branches.