The 26-year-old, who joined from Cardiff until the end of the season, has established himself as a regular in defence at Bramall Lane and manager Nigel Clough has already stated he would like to keep the full-back.
Brayford endured a frustrating start to life at Cardiff, failing to make a Premier League appearance before heading out on loan in pursuit of regular football in January.
Prior to making the switch to Cardiff, Brayford worked with Clough during his spells at Burton Albion and then Derby County, and he says their relationship was a big factor in his decision to drop down the divisions.
"I only really came here for the gaffer, having played for him at my two previous clubs," said Brayford.
"But I'm enjoying every minute of being here. I feel privileged to have been given the chance to play for this club.
"The lads in the dressing room are fantastic and the fans are different class.
"I would really welcome the chance to be here again next season because I have fallen in love with this club."