The deal is reported to be worth €55 million, which would represent the highest fee PSV have ever received for a player.
Saibari enjoyed an outstanding season in the Eredivisie, scoring 15 goals and providing eight assists in 27 appearances, 26 of them starts.
Bayern Munich's interest in the 25-year-old Morocco international first emerged in recent weeks, with head coach Vincent Kompany personally driving the move.
According to reports from Sky Germany, Bayern had initially proposed an offer in the region of €48 million, while PSV held out for closer to €60 million before the two clubs settled on a figure in between.
Saibari had already agreed personal terms with Bayern, and Romano now reports that all parties have reached agreement on the transfer itself.
The midfielder is currently in North America with Morocco for the World Cup, where he scored in the Atlas Lions' opening 1-1 draw with Brazil.
According to Romano, Saibari's medical examination will take place in the United States, made possible because Bayern's club doctor is already in the country working with the German national team.
Provided nothing unexpected arises during the medical, Saibari is then expected to be unveiled by Bayern Munich.
The deal will see Saibari sign a contract running until the summer of 2031, according to multiple reports from Germany and the Netherlands.
Bayern reportedly fought off interest from Paris Saint-Germain, who had made enquiries about Saibari earlier in the year before the German club moved decisively to secure his signature.
His Morocco teammate Bilal El Khannouss, who already plays in the Bundesliga with Stuttgart, spoke positively about the prospect of Saibari joining him in Germany.
"He's a very close friend of mine," El Khannouss said, while declining to comment further on the specifics of the move.
For PSV, the sale represents a significant financial boost and continues a pattern of developing talent before selling on for substantial fees.
For Saibari, the move represents a major step up, joining a club that will compete for the Bundesliga title and in the Champions League next season.
His World Cup performances with Morocco have only added to the sense that this transfer arrives at the perfect moment in his career, with Bayern getting their man just as his stock reaches its highest point yet.