The 34-year-old is expected to join Belgian side Standard Liege after a hugely frustrating spell at United, where he has not made a single appearance or even been given a shirt number this season.
The former Barcelona player posted a message on Twitter above a picture of United's training ground saying: "Thank you all for your support during these months of hard work for me. I will never forget! See you soon!"
Valdes signed an 18-month contract with United after moving to Old Trafford a year ago but fell out with manager Louis van Gaal over the summer.