Birmingham midfielder Charlee Adams has signed a new one-year contract with the club.
Southampton are confident Jay Rodriguez will commit to a new long-term deal but the player will consider his options.
The Republic of Ireland Under 21 international has come through the club's academy, but had been a target for Championship rivals Derby County and SPL champions Celtic.
However, the 20-year-old finalised a fresh deal with Leeds on Friday night and he is now looking forward to being part of manager Neil Warnock's plans for the coming season.
"It's fantastic to get everything sorted," White told Leeds' official website.
"I've been at the club since I was eight and I didn't want to leave. I came back in pre-season wanting to stay.
"I spoke to the manager who said he wanted me to stay and that we would try and get things done this week. That was a real positive and I'm looking to crack on for the season now."
White was shifted from his preferred left-back position to a roaming role on the right side of midfield following Warnock's arrival and admits he is happy to be a utility man.
"I've spoken with the gaffer and I think he sees that attacking role but also that I can play full-back if needed," White added.
"He talked about my being part of his plans, which was great. He has the experience, the squad he's building is more than capable and hopefully it will be an exciting season."