The 33-year-old, who picked up the injury during the Potters' 1-0 victory over Manchester City last month, is likely to miss the remainder of the campaign.
However, Odemwingie remains in a positive frame of mind and hopes to emulate the form he showed before suffering the setback upon his return.
"I'm happy the operation was successful, it's like a new beginning," the Nigeria international told BBC Sport. "I want to come back stronger than ever and hopefully pick up from where I stopped in August."
"I know it's going to be a long road back to kicking a football again but I am mentally prepared for that. You can't keep a good man down. It took couple of weeks to get the surgery done because I had to wait for the knee to settle down.
"Now that it's done I believe it will give me a new lease of life for the rest of my professional career."
Odemwingie joined Stoke from Cardiff City in January, scoring five goals in 15 league appearances at the back end of last season.