The 28-year-old will provide competition for Wes Foderingham, who has started all 21 of the Blades' Premier League matches this season.
The Croatia international, who joined Atletico in 2020, was back-up keeper to Slovenia captain Jan Oblak.
"I am really happy to be here. It is a big thing for every player to move to the Premier League. This is the best challenge for me," said Grbic.
"I'm sure it will be an amazing experience and it will be fun to play in front of our fans. I want to be involved as soon as possible.
"I've played in some good leagues in France and Spain, and played in the Champions League with Lille and played 15 or 16 games for Atletico last season which is a big club. I know I am ready now for this challenge."
The goalkeeper, who was part of Croatia's 2022 World Cup squad, is yet to make an appearance for club or country this season.
His contract at Atletico Madrid had been due to expire at the end of the season.
"There has been an enthusiasm to tie down a goalkeeper to a long-term deal," said Chris Wilder.
"We have done our homework on Ivo and we believe he can be an important member of our squad. We are looking forward to working with him."
The Blades are bottom of the Premier League and have won just two matches this season.