The defender, aged 25, was previously of Russian side Rubin Kazan but saw his contract at former Hull City manager Leonid Slutsky’s side suspended because of the Russian invasion of Ukraine.
A six-cap Croatian international, Uremović’s signing – just in time before the 5pm EFL deadline for registrations for the rest of the campaign - will bolster United’s depleted central defensive options after Chris Basham and Charlie Goode both picked up injuries recently.
"This is a really big club, and it is an honour and privilege to now have an opportunity to play here,” he said after signing for the Blades.
“I hope we will achieve our goals this season.
"It was a busy day on Saturday, I flew in from Croatia and watched the victory over Barnsley and it was an important three points. It was quite a good performance and we showed we were the better team.
"The atmosphere was really good, and I was happy to see so many people.
“It was a very quick deal after what happened with me in Russia last week, I got an offer from United, and I am very happy to be here."
Blades boss Paul Heckingbottom revealed Uremović has been a long-term target of United’s, but has always been out of their financial reach.
"Unfortunately, because of the terrible situation between Ukraine and Russia, players have had contracts suspended,” Heckingbottom added.