Musa, 28, leaves the Riyadh club with two years remaining of the four-year contract he signed when he joined from Leicester City.
He told ESPN that the decision to leave was entirely his own but both parties had come to an amicable, mutual understanding.
"I met with the club and requested that they should terminate my contract, and they were kind enough to agree to let me go," Musa told ESPN.
Al-Nassr announced Musa's departure on Sunday, when a farewell message on the Riyadh club's social media pages celebrated some of the goals scored by the Nigerian in his time in Saudi.
"Thank you Nigerian falcon, wishing you all the best in the future," Al-Nassr posted on Twitter.
Musa, one of the highest-paid players in Saudi Arabia, said that he had always expressed a desire to return to Europe.
"I have enjoyed my time in the two years that I have been here, and the club have been great to me," Musa told ESPN.
"But I have always wanted to return to Europe, and I feel that this is the best time for me to make that move.
"I want to get back to playing at the top level again against the best players in the world.
"I would like to thank everyone at Al-Nassr and all the fans for understanding and respecting my wishes, but especially for making me feel such a big part of the club and I will never forget them."
The Nigerian is now a free agent, which means he can join a new club immediately, and he told ESPN that his agent was "talking with some clubs in Europe".
"He knows what I want, so when there is something, I am sure he will let me know," Musa said.
Musa joined Leicester City for $21.45m as a then club-record signing in 2016 from Russian giants CSKA Moscow, but he found playing time -- and goals -- hard to come by; he scored just two goals in 21 league appearances.
He was loaned back to CSKA, where he re-established himself instantly with six goals in 10 league games.
He carried over that form to the international arena, scoring twice for Nigeria at the 2018 FIFA World Cup to become the country's top World Cup goalscorer before returning to England.
He was then transferred to Al Nassr, for whom he scored seven goals in 24 league appearances during his first season in Saudi Arabia.
Musa leaves Al-Nassr having scored 11 goals in 60 games.