The 26-year-old arrived at Banks's Stadium in August on non-contract terms before securing a deal until the end of the season.
And after a number of assured displays, Saddlers boss Dean Smith has secured the former Blackburn player's services for another 18 months.
"I'm really pleased that Andy has agreed this deal," Smith told the club's official website.
"He will be the first to admit that he came here with a lot of questions in his own mind having been out injured for a long period during his time at Sheffield United.
"But he has gone on to become a valuable member of the team here and has gradually built his fitness levels back up again.
"He's an experienced lad who has really helped the youngsters around him. He has put in a consistent level of performance for us and is also a great character and personality to have around the football club.
"This is another important piece of the jigsaw in place."
Taylor was released by Sheffield United in the summer after joining from Tranmere in 2009.
- Sports & Recreation
- Dean Smith
- Sheffield United