The deals see Warrior #208, Kennedy, and Warrior #306, Matthews, provide depth for the beginning of the 2020/21 season in positions where Glasgow Warriors are likely to lose multiple players for an extended period during the proposed international window.
Speaking to glasgowwarriors.org Kennedy said: "I've really enjoyed my time during both stints with the club. It's a great environment with a great group of people.
"The change in coaches is exciting and we still want to play some good fast rugby - I've always admired that about Glasgow.
"I'm really happy to have been given the chance to stay at the Warriors with everything that has been going on.
"All going well, I plan to stay fit and be ready to take my opportunity when it comes during this international window. I know what all the scrum-halves at this club can do and I'm looking forward to competing with such high-quality players for the nine jersey."
On Kennedy's extension head coach, Danny Wilson, said: "With the proposed international window it is evident we will need further cover at scrum-half as we could be without Ali (Price) and George (Horne) for an extended period of time.
"I have been impressed with Sean watching him from afar. He has trained well during this recent period and I'm looking forward to continuing to work with him over the coming months."
Matthews, 27, initially joined the Warriors from Boroughmuir on a three-month deal at the beginning of the 2019/20 season.
A try-scoring performance against Ulster in pre-season and outings against the Toyota Cheetahs, Cardiff Blues and Dragons impressed the Glasgow coaches and saw Matthews earn a contract extension through to the end of the 2019/20 season.
Speaking to glasgowwarriors.org the Scotland Club XV cap said: "It's a great privilege and honour to be able to get the chance to continue playing for this club.
"My mums' side of the family is from Glasgow and it brings a lot of pride to pull on the jersey and play with some fantastic players.
"I've really enjoyed working with the new coaching group, including Danny and Kelly (Brown).
"This coming season is a chance for us to get some more good results. I want to make the most of the international window and try to get a run of games together to show what I can do on the pitch."
On the announcement of the Matthews contract extension head coach Wilson said: "There is a strong possibility we will lose hookers to both Scotland and Fiji during the international window and again being able to retain a Scottish talent that has been part of the Warriors squad is a boost ahead of the new campaign. "Johnny has gone well in the past for the Warriors and has been training well during the most recent window."