Sadio Mane featured in Bayern's pre-season friendly with Manchester City in Tokyo last month
The 31-year-old scored 12 goals in 38 games for Bayern in an underwhelming season despite initially impressing.
The Senegal player was also involved in a physical altercation with Leroy Sane in the Manchester City dressing room after losing a Champions League game.
Reports suggest the German champions have recouped most of the £35m they paid Liverpool for Mane a year ago.
Bayern CEO Jan-Christian Dreesen said the former Southampton player - who has signed a four-year deal with Al-Nassr - had not had an "easy year" since moving from Anfield.
"He was not able to contribute as much as we all and he himself had hoped," said Dreesen.
Earlier on Tuesday Bayern manager Thomas Tuchel said he and Mane agreed "it was the best solution to untie the knot".
"We had a long, big hug and we both agreed we don't like what's happening now, but we think it's for the best in this situation," said the Bayern coach.
"Sometimes things don't work out as everybody wants. I have always had a very good relationship with him and this will stay.
"I can totally understand he feels hurt and I also wouldn't feel happy if things like this happened.
"Obviously it's something that we didn't bring into the full potential, which is my responsibility, but in this particular situation it was the best solution to untie the knot."
Al-Nassr signed five-time Ballon d'Or winner Ronaldo in December and have followed that up this summer by adding Croatia midfielder Marcelo Brozovic, Brazil full-back Alex Telles and Ivory Coast midfielder Seko Fofana.
-- Courtesy of BBC Sport