The defender arrives at the Utilita Energy Stadium on a permanent basis initially until the end of the 2020/21 season - following a successful trial period - after cancelling his contract at Italian outfit Como.
Born and raised in Bradford, the 22-year-old began his career within City's academy, before a spell with Bury and four years at top-flight Everton - where he won Premier League 2 twice and the Premier League Cup.
A left-back who can also operate in central defence, Foulds told Bradford's website: “I am over the moon to be joining such a big club which I have supported all my life.
“Since leaving as a youngster, I always had dreams of coming back after watching the likes of Nahki Wells and James Hanson scoring goals - from the stands - so it is a bit of a dream come true, for me.
“The standard in training over the week or so I have been here has been top notch, and I have really enjoyed myself so far. The lads have welcomed me with open arms and been brilliant, so I have settled in straight away.
“It is only initially until the end of the season, but I am looking forward to showing what I can do and hopefully helping get this club where it needs to be."