The 26-year-old, who has been capped at Under-19, Under-21 and 'A' level for Ireland, is delighted to extend his stay at the Sportsground.
"I have really enjoyed my time with Connacht and I am looking to the seasons ahead as we build on the progress we have made," he said.
Matthews is the fifth player to re-sign for Connacht in the past month, after senior internationals Gavin Duffy and Johnny O'Connor and soon-to-be Irish-qualified duo Brett Wilkinson and Ray Ofisa put pen to paper on new deals.
The busy Connacht management also recently secured the services of lock Bernie Upton from North Harbour in New Zealand. Upton will link up with the squad in the summer.