Sanchez, who spent two seasons with the Reds scoring 19 goals in 57 games, came off the bench to score Adelaide's third goal in their 3-1 Grand Final win over Western Sydney Wanderers last Sunday.
Post-Grand Final, Reds striker Bruce Djite urged the club - LIVE on air - to re-sign Sanchez but it proved fruitless.
"My time at Adelaide United was very good," Sanchez said.
"Last season we won the FFA Cup in my first year at United and it was an amazing year because I also won the Golden Boot.
"This season just passed was fantastic as well for how we came back from a slow start and then we won the Premiership and the Championship.
"The way we won this season made it more important because we stayed together and worked very hard in the difficult times and got the rewards for our sacrifice.
"Scoring in the grand final was the icing on the cake for me and I will always remember this moment.
"It was one of the most important moments in my life alongside my wedding and the birth of my son.
"I will never forget Adelaide and I want to come back one day, to enjoy the club and the people here, that I love."
Sanchez, who netted nine times in 2015-2016, joins Craig Goodwin (Sparta Rotterdam), Eli Babalj (returned to AZ after loan spell ended) and fellow Grand Final goalscorer Bruce Kamau (Melbourne City) in departing Guillermo Amor's side since the championship success.
