The former Scotland international saw his contract at The Hawthorns terminated by mutual consent just as the transfer window was closing on Monday.
By releasing him at that time, Snodgrass now has until March to sign for another club.
But in a statement released on Instagram, the former West Ham man expressed his disappointment that his time with the Baggies has come to an end early.
Snodgrass has been blighted by injury since becoming Sam Allardyce's first Albion signing a year ago.
He has also struggled for fitness this year.
But a falling out with head coach Valerien Ismael is believed to be a key reason why he has only featured seven times this season.
Speaking on social media account, Snodgrass thanked Albion's players, fans and staff for the support they have given him over the past 12 months.
Ismael, though, did not get a mention.
“I want to thank @wba for giving me the opportunity,” Snodgrass said via his Instagram account.
“From the very 1st day I arrived I was made to feel welcome, the support from the fans was superb, the players are top lads, the medical team and sports science, canteen staff, kit-men and kit ladies, receptionist and security, I wish you all nothing but best wishes.
“I am gutted to be leaving, but this was a very difficult few months for me. I want to wish the club all the best for the future, and hope to see the boys get promoted.
“I am excited for the next challenge in my career.”
Snodgrass has made a combined 573 career appearances with Livingston, Stirling, Leeds, Norwich, Hull, West Ham, Villa and the Baggies, scoring 110 goals.
In a statement, announcing his departure, Albion said: "The club thanks Robert for his efforts and wishes him well in his future career."