Welker was injured in the first quarter Sunday against the Texans when he tried to plant his left foot after making a catch. He was helped to the sideline by members of the Patriots' medical staff, then buried his head in a towel while sitting on the bench and was later carted to the locker room.
While the Patriots have yet to announce the specifics of Welker's injury, initial tests showed he tore both the anterior cruciate ligament and medial collateral ligament in his left knee, a source close to the situation told ESPN NFL Insider Adam Schefter on Sunday.
Welker thanked fans and friends for their support on Wednesday in a statement posted on his charitable foundation's website, 83foundation.com.
"My good friend Tedy Bruschi said to me the other day, 'There is no career without a comeback.' Although I know that it will take time to be the same player that I once was, I am ready to face that challenge, and in time, I plan on coming back the player I was and much more," Welker said in the statement.
"This is not the first time that I have faced adversity in my career, and it won't be the last. I am committed to this football team and doing everything possible to make us better. My teammates know my commitment to them, and I refuse to let them down."
Welker finished the season with a franchise record 123 catches (despite missing two games), 1,348 yards and four touchdowns.
"You can't replace him, there's no doubt about that," Tom Brady said Monday in an interview on Boston sports radio station WEEI. "There's nobody that can substitute in for Wes and think that they're going to be Wes. He is everything you ask for.
"We've got to move on and we've got to go out there and play, and everyone I think in different areas has to pick it up. I have to play better, Julian [Edelman] has to play better, Randy [Moss] has to play better, the offensive line, running backs, tight ends, we all have to do more. I think that's the commitment we have to make to one another."
The Patriots also announced that linebacker Thomas Williams has been signed from the practice squad to the 53-man roster.