The 22-year-old joins on a permanent deal, after cancelling his contract with Italian side Como.
The Bradford-born player began his career with the club's academy, before joining Bury and then moving onto Everton, where he won the Premier League 2 twice and the Premier League Cup.
Foulds joins the Bantams after a successful trial period and can provide versatility across the back four, having the ability to operate at left-back and in central defence.
“I am over the moon to be joining such a big club which I have supported all my life," he said.
“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.”
City’s joint-interim bosses, Mark Trueman and Conor Sellars, added: “We have had Matty in for the past week or so and been really impressed by what we have seen.
“His attitude and application has been first class, and he has a lot of ability with potential to get much better - while still at a young age.
“He took it upon himself to leave Como and come on trial with us, which gives a good measure of how desperate he was to join.
“With him being born and raised in Bradford, we have kept tabs on him for quite some time, and watched a lot of him during his four years at Everton - where he developed well.
“He is determined to succeed at Bradford City, so we are really looking forward to seeing him in action.”
Bradford are not in action today after their League Two fixture with Crawley Town was postponed due to dangerous weather conditions surrounding their Valley Parade Stadium.
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