Sources have told ESPN FC that Boateng's deal includes a fee of €1 million and has an €8m option to make the move permanent in the summer.
A statement on the Catalan club's website read: "His ability to bring people into the game means he is excellent at playing behind the main striker."
Sassuolo hailed the move as another positive step in their relationship with the Camp Nou side.
"This furthers the profitable relationship between Barcelona and Sassuolo, born this summer as part of the buying and selling of the footballer Marlon," read a statement on the Serie A club's website. "The Catalan club thank the Italian club for their openness in conducting these negotiations.
"The Italian club, on their part, express how very proud they are to be able to continue this relationship with one of the biggest and most prestigious clubs in the world."
Before the deal was announced, Boateng told Sky Sport Italia that he'd already bid farewell to Sassuolo leadership.
"I'm a bit sad because I'm leaving a professionally-run club in Sassuolo and it was hard to say goodbye to everybody today, even if Barcelona are one of the biggest clubs in the world," Boateng told the outlet.
"It was a testing day, but saying goodbye to my teammates, [sporting director Giovanni] Carnevali and the coach meant so much to me.
"I've got a lot of respect for this side and that is why I had to say my goodbyes in person."
Boateng, 31, arrives to bolster Barca's forward line after the sale of Munir El Haddadi to Sevilla earlier this month.
Munir's exit left the La Liga leaders without a backup for Luis Suarez and coach Ernesto Valverde has been open about his desire for the club to add another body in January.
A number of options were looked at but ruled out for various reasons.
Girona's Cristhian Stuani was deemed too expensive as a short-term option, Alvaro Morata preferred a move to Atletico Madrid where he's been guaranteed more football and Los Angeles FC's Carlos Vela was discarded at the last minute because he's not played competitively since November.
Boateng's arrival is even more timely given confirmation that Ousmane Dembele is set to be sidelined for the next 15 days with a sprained ankle. The France forward's injury further reduces Valverde's attacking options going into the two-legged Copa del Rey quarterfinal against Sevilla and league games against Girona and Valencia.
After starting his career at Hertha Berlin, in the city where he was born, Boateng, whose brother Jerome plays for Bayern Munich, has spent time in England, Italy, Spain and back in Germany.
Following spells with Tottenham, Borussia Dortmund and Portsmouth, he played some of the best football of his career during a three-year stint with Milan between 2010 and 2013.
Since then, he's represented Schalke, Milan (again), Las Palmas, Frankfurt and Sassuolo, who he joined last summer. In 15 appearances for the Italian side this season, operating primarily as a centre-forward, he's impressed, scoring five goals despite a period out injured.
While not an obvious January signing for the La Liga leaders, he fits all the requirements the club had drawn up. He has top-level experience, knowledge of the Spanish league, is prepared to accept a backup role and is available for relatively cheap on a short-term deal.
The signing of Boateng could also have repercussions elsewhere at Barca. Denis Suarez, despite Valverde's reluctance to let him go, is still keen on a move to Arsenal, while the club are open to offers for Brazil forward Malcom.
Information from ESPN FC's Ben Gladwell and James Horncastle was used in this report.