The 28-year-old DR Congo international has been the number one target for Newcastle since it became clear their striker Alexander Isak wanted to join Liverpool.
Isak was poised to complete a British record 125 million-pound move to the Premier League champions on Monday.
Wissa scored 45 goals in 137 Premier League appearances for Brentford since arriving from French club Lorient, but has not featured this season as he held out for a move.
Last week, he issued a statement via social media pleading with Brentford to allow him to join Newcastle.
Wissa, who had two years of his contract remaining at Brentford, is expected to have a medical at Newcastle later on Monday before completing his move.
His arrival will be a boost to Newcastle manager Eddie Howe, whose side have had two 0-0 draws in their opening three games.