The news follows hooker Tom McCartney's decision to commit to the Irish province for a further three seasons.
Highly-rated prop Buckley, Ireland second row Roux and fly-half Carty have all agreed new two-year deals.
There were fears of a possible player exodus following coach Pat Lam's announcement that he will take over at Bristol at the end of this season.
"Having witnessed the three of them grow and develop as players and men over the past four seasons, I'm personally very pleased that they will be part of a strong squad that will drive continued success on and off the field for Connacht," said Lam.
Roscommon natives Buckley, 26, and Carty, 24, are both products of Connacht Academy and have made 103 and 67 appearances respectively for the province.
Carty was Connacht's hero on Saturday evening when he kicked the injury-time conversion which helped the Irish province earn a vital 20-18 European Champions Cup win over Wasps.
Former Leinster lock Roux, 26, is in his third season at the Sportsground club and made his Ireland debut against his native South Africa in June.
All three helped Connacht clinch a remarkable Pro12 title triumph last season.
Connacht's star centre Bundee Aki, who is also a New Zealander, signed a contract extension earlier this season which will keep him at the Irish province until 2020 and he will become Irish-qualified next October.
Denis Buckley, Jack Carty and Quinn Roux have become the latest Connacht players to agree contract extensions.