The Blades manager led the team to the League One title last season, having guided Northampton Town to the League Two title in 2015-16.
Wilder, who had two years remaining on his deal, had been linked with managerless Sunderland.
"I'm delighted and proud to manage this football club," he told BBC Radio Sheffield.
"There's been talks right from the end of last season and I think we've agreed a deal in principle to extend my contract by another year.
"I had two years left so it was up to the owners to come to me and fair play they have done - and I've been comfortable with how it's been handled.
"Everyone knows my affection for this football club and I am ambitious and I want to achieve all my ambitions here."
The Blades have added four players so far this summer as they prepare for their first season back in the Championship after six seasons in the third tier.
Wilder said the club are also hoping to secure moves for Charlton midfielder Ricky Holmes and Southend midfielder Ryan Leonard.
"I think it's common knowledge we have bids out for Ricky and Ryan, but we understand that these deals don't always get completed," he said.
"Some players you get in quickly and it's easy and some take a bit of time. You can reach a point where you have to move on.
"We want players in quickly but sometimes you have to be patient. Some of the best business we did last year was in August."
Sheffield United boss Chris Wilder has said he has agreed a contract extension "in principle".