The 30-year-old has played at Goodison Park for his entire career, only leaving on loan for short spells at Carlisle United and Derby County.
Moyes, who handed Osman his debut against Tottenham Hotspur in 2003, has hailed the achievement of reaching 300 appearances and hopes that there is more to come.
"He's done really well since near enough when I started," said Moyes. "I remember when I came, I put him out to Carlisle on loan and then to Derby County. After that, he has been in and around the first team.
"He's an intelligent player who can create things and play several different roles He's someone we can rely on and he's very well respected here.
"He's been a really good servant and I think it's a great achievement to get to 300 games. Well done Ossie. We hope there's more to come."
Osman should be a part of Everton's plans for the visit of Fulham tomorrow afternoon.