Browne is a younger brother of former Connacht favourite and current Brive lock Damien Browne. He ame through the Connacht Academy system in 2007.
He has enjoyed regular game-time since then, winning 45 Magners League caps and 16 Amlin Challenge Cup caps.
The 6ft 5in, 112kg forward has played at blindside flanker this season in the absence of John Muldoon, but is equally as comfortable in the second row.
His power and athleticism have made him something of a lineout specialist and he has been an integral part of the Connacht pack this season, featuring in 19 games so far.
Browne, who won his first cap for O2 Ireland Wolfhounds last month, was part of the Ireland Under-20 side that won the Grand Slam in 2007 alongside fellow Connacht players Jamie Hagan, Ian Keatley, Aidan Wynne and Shane Monahan.
"Playing rugby in your home town is great. Growing up in Galway and playing youth rugby here, it was always my goal to play for the province," he said.
"Having come up through the Academy getting my first contract was a dream come true, so I am delighted to be able to commit to Connacht for another two years.
"There's something special about playing for Connacht, everyone gets on really well and there's a great buzz about the place, especially this year when things are starting to go our way a bit more.
"The coaching set-up here is world class and I'm very happy to be playing here for the foreseeable future."
The talented 20-year-old centre/winger played much of his youth rugby with Galway Corinthians and has made regular appearances for their Ulster Bank League Division 2 side.
He won nine caps with the Ireland Under-20s, scoring tries against Argentina and Samoa in the IRB Junior World Championship last year. He also touched down against Wales and England in the Six Nations title-winning campaign.
Griffin received the man-of-the-match award for his part in Connacht's 26- 22 victory over Samoa last November and was a try scorer in the province's derby defeat to Leinster on New Year's Day.
The 6ft 1in, 94kg back's progression has been hampered by injury this season but his raw pace and eye for a gap means he is never far from the coaches' minds.
"To be part of the Connacht set-up as a Galway-man is fantastic. You always hope that you'll make it and though I've always been confident in my ability, to be given the opportunity to prove myself is superb," explained Griffin.
"The Academy set-up is very good under Nigel Carolan and I've received some top quality coaching that has prepared me really well for the step up to Magners League level.
"I was delighted to be given the chance to show what I can do at the start of the season and to be awarded my first full professional contract here at Connacht means a huge amount to me.
"I will continue to learn for the more experienced guys in the squad and hope to continue developing my own game here at Connacht."
Commenting on the deals for Browne and Griffin, Connacht Academy manager Nigel Carolan said: "It's nice to see two local lads come from grassroots to the professional set-up through the Academy system.
"I feel that they recognise the importance of Connacht in the future of Irish and European rugby, and are committed in promoting the province to the next level."