Mutch, still only 28, arrives after spells in South Korea and the USA on a free transfer. He has signed to the end of 2020.
"Jordan is a class player who has the potential to become the best midfielder in the Eliteserien.
"In addition to being a good football player, he is also a good type that will fit well in the squad," said Aalesund sporting manager Bjørn Erik Melland.
Mutch had been with Gyeongnam FC in the K-League.