The Championship club have secured the 27-year old German striker on a one-year deal with the option of a further two years.
Proschwitz heads to Griffin Park after scoring just seven goals in 37 appearances for the Tigers following his July 2012 move from SC Paderborn.
"We have had a long search to find the right striker that offers us quality and a variety of weaponry," Bees boss Mark Warburton told the club's official website.
"Nick is a very experienced player. He put in some fantastic performances in Germany before his move to Hull.
"He went on loan to Barnsley at the end of last season and scored four in eight.
"He is an aerial threat and has very good technical ability. We think he will bring outstanding quality to the squad.
"We are delighted to secure him and look forward to him playing an important part this season."
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