Sessegnon, 26, the Benin international attacking midfielder, signed a three-and-a-half year deal after signing for 7 million euros.
Muntari previously played in the Premier League with Portsmouth before moving to Inter in July 2008. The 26-year-old midfielder joins Ghana team mates Asamoah Gyan and John Mensah at Sunderland, who are currently sixth in the table.
Inter replaced Muntari with Moroccan midfielder Houssine Kharja on loan from Genoa until the end of the season.
The additions of Muntari and Sessegnon will boost Sunderland's squad after they sold striker Darren Bent to Aston Villa for 18 million pounds this month.
'LITTLE POWERHOUSE'
"Stephane can play on the left, on the right, through the middle - he's lightning quick and he's a match-winner," Sunderland manager Steve Bruce told the club's website.
"He's a little powerhouse with a small centre of gravity, some great dribbling skills and a good shot.
"I think he'll be a big hit with the supporters. I predict he'll turn into a crowd favourite.
"His ability to slot in across attacking positions makes him a great addition to what is a young and hungry squad."
Bruce was equally happy to have gained the services of Muntari for the rest of the season, one of the north-east club's most successful for years.
"Sulley is a fabulous acquisition for the club. When the opportunity arises to bring in a player of his ability - even in the short term - you have to take it, and I'm delighted we have been able to," he said.
"His adaptability is a great asset. He did extremely well at Portsmouth so he knows the league well and you have to be some player to move to Inter Milan for the fee that he did (16 million euros)."
Kharja is likely to be a squad player at the San Siro having failed to shine at Genoa, but injuries to Wesley Sneijder and Dejan Stankovic mean he could be used in Inter's game against Palermo on Sunday, alongside fellow new signing Giampaolo Pazzini.
The European champions, who brought in Genoa defender Andrea Ranocchia at the start of the January transfer window, have also said they are interested in Feyenoord striker Luc Castaignos but that any deal would be done in the close-season.
‘Maybe I’ll be signed by Wrexham, who knows? English football would suit me – if an offer came, I wouldn’t think twice, I’d go immediately’ Euro 2024 cult hero reveals his UK dream
‘Managing Leeds? It was an option that appeared, but it wasn’t the right timing. I decided it wasn’t a good idea to leave the club I was at mid-season’: Premier League boss admits to turning down opportunity to replace Jesse Marsch in 2023
