The Jazz had until Wednesday to make the offers and keep the right to match offers from other teams for the restricted free agents.
Utah made the offers Monday. Terms were not disclosed.
Matthews played in all 82 games last season as a rookie, when he made the team as an unrestricted free agent. He started 48 games and averaged 9.4 points, 2.3 rebounds and 1.5 assists.
Fesenko became a starter when Mehmet Okur tore his Achilles' tendon in the playoff opener at Denver. He has played three years with the Jazz and appeared in 49 games last season.