Ofisa, whose brother Treviranus also played for Connacht, has been capped by the province 80 times and will remain at the Sportsground until 2012.
"I'm really pleased to extend my time here with Connacht, Galway has become a home away from home and the standard of rugby here is exceptional," he said.
"To be involved with Connacht for another season allows me to keep testing myself at the highest level possible."
Adrian Flavin, who signed for Connacht in 2006 from London Irish where he amassed 84 caps, has represented the province 68 times in the Magners League and 23 times in the Amlin Challenge Cup.
The former Ireland Under-19 and Under-21 hooker was capped twice by Ireland 'A' in 2008 against England and Scotland.
Flavin has 94 caps for Connacht to date and captained the side in their historic victory over the Samoan national team last November. He has signed a new contract which will see his remain at the Sportsground until 2013.
"Working under Eric (Elwood) and Dan (McFarland) is both challenging and rewarding and the squad are fantastic to train and play alongside, so I'm very happy to commit to the province for the next two years," admitted Flavin.
"There's a real sense of belief in the squad and it's great to be a part of that and the stability of a two-year contract allows me to focus on training and being the best rugby player I can be."
Michael Swift is Connacht's most capped player of all-time. He joined Connacht in 2000 from English club Richmond where he made six Premiership and two Challenge Cup appearances.
The Hammersmith-born second row quickly established himself as a favourite with fans at the Sportsground for his immense work-rate and dedication.
Standing at 6ft 5in and weighing 119kg, 'Swifty' is one of the most physically imposing players in the squad and his record haul of 190 caps for Connacht to date shows no sign of slowing up.
In fact, Swift is on course to be the first player in Connacht's history to reach 200 caps. He has signed a one-year deal with the province which will keep him at the Sportsground until 2012.
"I am delighted to extend my contract with Connacht. I have really felt at home here since my move eleven years ago," he said.
"It is an honour to be Connacht's most-capped player. The fans have been terrific during my time here and I hope I can repay their support and continue to serve Connacht as best I can."
Connacht head coach Eric Elwood added: "We are very pleased with the re-signing of Swifty, Flav and Ray. They have been great servants to Connacht Rugby and we are delighted they have shown their loyalty to the province by extending their contracts."