Martinez, 26, once pledged his loyalty to the San Sebastian club having risen through the ranks by saying he would "never go to the other side".
But his words proved hollow on Tuesday as he completed a club-record 32 million euro (28.04 million pounds) switch to Athletic.
"From tomorrow afternoon Real Sociedad will offer fans who don't want to wear the name of Inigo Martinez on their shirts the chance to swap it for this season's shirt with the name they want, completely free of charge," said a message on the club's website, titled "Now he's history".
The audacious transfer was achieved through Athletic selling Aymeric Laporte to Manchester City for 65 million euros, allowing them to pay Spain international Martinez's release clause.
Sociedad at least had the cash to sanction the shirt gesture to their supporters who had watched Martinez's progress over seven years at the club.
(Reporting by Richard Martin, editing by Christian Radnedge)
