The Blades defender, 30, has extended his contract at Bramall Lane until 2021, and is due to return from suspension for Friday night’s Steel City derby.
"There's nowhere else I'd want to go and play, this club is definitely on the up and I really want to be a part of it for the next two-and-a-half years,” he said.
"I've been here a long time, my family love the city and with them settled I'm able to focus on my game and playing consistently well, hopefully we can enjoy a double celebration on Friday night."
"I'm really pleased it's sorted. The manager knows I'm a thinker and now I can focus on arguably the biggest game of the season so far."
Basham - who has played over 200 games for United - has become an integral part of Chris Wilder’s Blades, having joined from Blackpool in 2014.
“We have always made the point that if players deserve a new contract then they will be rewarded and that is certainly the case with Chris," said Wilder.
"His performances whilst I've been at the club, and before that, have been exceptional and I'm delighted he has committed to us for the next couple of years.
"Bash is an excellent character, an athlete and as a footballer he has moulded seamlessly into our style of play."