Saibari emerged as Vincent Kompany's priority target after an exceptional campaign with PSV, which saw him produce an eye-watering 28 goal involvements in 37 appearances.
The Moroccan, who is set to star at this year's World Cup in North America, agreed a contract until 2031 with the Bundesliga giants on Wednesday.
Bayern just needed to agree on a transfer fee on the 26-year-old after submitting an opening bid of €48m, and according to Fabrizio Romano, a deal is now entering the "final stages".
Saibari will have his medical in the United States before signing a five-year contract at the Allianz Arena and becoming Kompany's first signing of the summer.
Romano didn't state whether the two clubs have negotiated a final fee for the fleet-footed Moroccan, but it should be closer to PSV's €60m valuation of the player.