Sibley, 19, broke into the Rams' first team last season, making 11 Championship appearances and six more in cup competitions and scoring five goals including a hat-trick against Millwall.
Bird, for whom the contract comes a day before his 20th birthday, made four league appearances in 2018-19 and began to hold down a regular place last season, recently deputising as captain in the absence of Wayne Rooney.
He told Rams TV: "For myself, (the aim is) just to kick on again, have a full season in the first team, and take the team and the club where it should be – and that's at the top end of the table.
"Whether it's play-offs or whether it's automatic promotion, that needs to be in our sights. We need to get promoted this season."
Sibley added: "I always knew there was the pathway at Derby. Birdy's been a bit longer in the first team but I've had the chance last season and took it.
"I want to be a key player, playing every week. For both of us, we want to keep proving what we can do.
"Like Birdy said, we've got a good group of lads so hopefully this season we can push for the play-offs. Last season was a bit unfortunate but hopefully this season we can go for it."