Liddle, 27, has signed a one-year deal with the option of an extra year and will become a Bantam on July 1 when his Notts County contract expires.
He told Bantams Player: "Phil (Parkinson) rang me pretty soon after the news got out that I was leaving Notts County and I was delighted to see his name flash up on my phone.
"Straight after my meeting with him, I was speaking to my agent and my family telling them that this is the manager and this is the club I want to play for.
"As soon as the manager told me of his plans for next season, it was something I wanted to be a part of."
Player of the year Darby, whose current deal was set to expire, will replace Gary Jones as the new skipper of the side having penned a contract until the end of the 2016/17 season.
Darby said: "I'm delighted to have signed a new three-year deal here and I can't wait to help the club keep progressing forward.
"It is a massive honour and such a privilege to be given the captain's armband, especially when you look at some of the names of other Bradford City captains down the years."
The Bantams also announced that Nathan Doyle has left the club after his contract expired.
The 27-year-old began a second spell with City in 2012 but departs after 94 appearances.